Travelling waves

Shifting the position, turning standing waves into travelling waves, another way to make waves travel, the speed of a wave on a string, for more information.

Travelling Wave

When something about the physical world changes, the information about that disturbance gradually moves outwards, away from the source, in every direction. As the information travels, it travels in the form of a wave. Sound to our ears, light to our eyes, and electromagnetic radiation to our mobile phones are all transported in the form of waves. A good visual example of the propagation of waves is the waves created on the surface of the water when a stone is dropped into a lake. In this article, we will be learning more about travelling waves.

Describing a Wave

A wave can be described as a disturbance in a medium that travels transferring momentum and energy without any net motion of the medium. A wave in which the positions of maximum and minimum amplitude travel through the medium is known as a travelling wave. To better understand a wave, let us think of the disturbance caused when we jump on a trampoline. When we jump on a trampoline, the downward push that we create at a point on the trampoline slightly moves the material next to it downward too.

When the created disturbance travels outward, the point at which our feet first hit the trampoline recovers moving outward because of the tension force in the trampoline and that moves the surrounding nearby materials outward too. This up and down motion gradually ripples out as it covers more area of the trampoline. And, this disturbance takes the shape of a wave.

Following are a few important points to remember about the wave:

  • The high points in the wave are known as crests and the low points in the wave are known as troughs.
  • The maximum distance of the disturbance of the wave from the mid-point to either the top of the crest or to the bottom of a trough is known as amplitude.
  • The distance between two adjacent crests or two adjacent troughs is known as a wavelength and is denoted by 𝛌.
  • The time interval of one complete vibration is known as a time period.
  • The number of vibrations the wave undergoes in one second is known as a frequency.
  • The relationship between the time period and frequency is given as follows:
  • The speed of a wave is given by the equation

Different Types of Waves

Different types of waves exhibit distinct characteristics. These characteristics help us distinguish between wave types. The orientation of particle motion relative to the direction of wave propagation is one way the traveling waves are distinguished. Following are the different types of waves categorized based on the particle motion:

  • Pulse Waves – A pulse wave is a wave comprising only one disturbance or only one crest that travels through the transmission medium.
  • Continuous Waves – A continuous-wave is a waveform of constant amplitude and frequency.
  • Transverse Waves – In a transverse wave, the motion of the particle is perpendicular to the direction of propagation of the wave.
  • Longitudinal Waves – Longitudinal waves are the waves in which the motion of the particle is in the same direction as the propagation of the wave.

Although they are different, there is one property common between them and that is the transportation of energy. An object in simple harmonic motion has an energy of

Constructive and Destructive Interference

A phenomenon in which two waves superimpose to form a resultant wave of lower, greater, or the same amplitude is known as interference. Constructive and destructive interference occurs due to the interaction of waves that are correlated with each other either because of the same frequency or because they come from the same source. The interference effects can be observed in all types of waves such as gravity waves and light waves.

Wave Interference

According to the principle of superposition of the waves , when two or more propagating waves of the same type are incidents on the same point, the resultant amplitude is equal to the vector sum of the amplitudes of the individual waves. When a crest of a wave meets a crest of another wave of the same frequency at the same point, then the resultant amplitude is the sum of the individual amplitudes. This type of interference is known as constructive interference. If a crest of a wave meets a trough of another wave, then the resulting amplitude is equal to the difference in the individual amplitudes and this is known as destructive interference.

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There's another COVID variant you should know about: KP.3 now makes up 25% of COVID cases

travelling wave exponential

The Centers for Disease Control and Prevention data shows that a new COVID variant, the KP.3 variant , is rising to dominance across the United States.

For the two-week period starting on May 26 and ending on June 8, the government agency data shows that KP.3 accounts for 25% of COVID cases in the U.S. and is now the dominant variant. This knocks down previous frontrunner, the JN.1 variant , which spread globally last winter. KP.2 is right after KP.3 and now makes up 22.5% of cases.

The CDC uses Nowcast data tracker to project the COVID variants over a two-week period. The tool is used to help estimate current prevalence of variants, but does not predict future spread of the virus, the CDC said.

Could there be a summer surge?: New COVID-19 FLiRT variants are now the dominant variant.

What is the KP.3 variant?

Like JN.1 and "FLiRT" variants KP.1.1 and KP.2, KP.3 is a similar strand.

USA TODAY reached out to the CDC for more information on the variant but have not heard back.

State of COVID cases in US

Although the rates for deaths and hospitalizations have declined significantly, the data also shows that the rates for positive tests and emergency room visits are on the rise.

The CDC recently reported on June 4 that "COVID-19 infections are growing or likely growing in 30 states."

COVID fall vaccine will target JN.1

The dominant emergence of the KP.3 variant comes on the heels of an FDA panel meeting this week to discuss updates to a COVID vaccine for the fall.

During the Vaccines and Related Biological Products Advisory Committee , health experts from vaccine manufacturers Pfizer, Moderna and Novavax each told the panel they were prepared to make JN.1-targeted vaccines available in August pending FDA approval.

The updated vaccines are set to be  released in the fall , ahead of expected winter upticks in COVID-19 cases.

Contributing:   Eduardo Cuevas , USA TODAY.

Ahjané Forbes is a reporter on the National Trending Team at USA TODAY. Ahjané covers breaking news, car recalls, crime, health, lottery and public policy stories. Email her at  [email protected] . Follow her on  Instagram ,  Threads  and  X (Twitter) .

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2.3: Representation of Waves via Complex Functions

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  • Page ID 15731

  • Richard Fitzpatrick
  • University of Texas at Austin

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In mathematics, the symbol \({\rm i}\) is conventionally used to represent the square-root of minus one: in other words, one of the solutions of \({\rm i}^{\,2} = -1\). Now, a real number , \(x\) (say), can take any value in a continuum of different values lying between \(-\infty\) and \(+\infty\). On the other hand, an imaginary number takes the general form \({\rm i}\,y\), where \(y\) is a real number. It follows that the square of a real number is a positive real number, whereas the square of an imaginary number is a negative real number. In addition, a general complex number is written \[z = x + {\rm i}\,y,\] where \(x\) and \(y\) are real numbers. In fact, \(x\) is termed the real part of \(z\), and \(y\) the imaginary part of \(z\). This is written mathematically as \(x={\rm Re}(z)\) and \(y={\rm Im}(z)\). Finally, the complex conjugate of \(z\) is defined \(z^\ast = x-{\rm i}\,y\).

Just as we can visualize a real number as a point lying on an infinite straight-line, we can visualize a complex number as a point lying in an infinite plane. The coordinates of the point in question are the real and imaginary parts of the number: that is, \(z\equiv (x,\,y)\). This idea is illustrated in Figure [f13.2] . The distance, \(r=(x^{\,2}+y^{\,2})^{1/2}\), of the representative point from the origin is termed the modulus of the corresponding complex number, \(z\). This is written mathematically as \(|z|=(x^{\,2}+y^{\,2})^{1/2}\). Incidentally, it follows that \(z\,z^\ast = x^{\,2} + y^{\,2}=|z|^{\,2}\). The angle, \(\theta=\tan^{-1}(y/x)\), that the straight-line joining the representative point to the origin subtends with the real axis is termed the argument of the corresponding complex number, \(z\). This is written mathematically as \({\rm arg}(z)=\tan^{-1}(y/x)\). It follows from standard trigonometry that \(x=r\,\cos\theta\), and \(y=r\,\sin\theta\). Hence, \(z= r\,\cos\theta+ {\rm i}\,r\sin\theta\).

clipboard_e9ac70c9f118e30f1751f0b328e55a13e.png

Figure 3:   Representation of a complex number as a point in a plane.

Complex numbers are often used to represent wavefunctions. All such representations depend ultimately on a fundamental mathematical identity, known as Euler’s theorem , that takes the form \[{\rm e}^{\,{\rm i}\,\phi} \equiv \cos\phi + {\rm i}\,\sin\phi,\] where \(\phi\) is a real number. Incidentally, given that \(z=r\,\cos\theta + {\rm i}\,r\,\sin\theta= r\,(\cos\theta+{\rm i}\,\sin\theta)\), where \(z\) is a general complex number, \(r=|z|\) its modulus, and \(\theta={\rm arg}(z)\) its argument, it follows from Euler’s theorem that any complex number, \(z\), can be written \[z = r\,{\rm e}^{\,{\rm i}\,\theta},\] where \(r=|z|\) and \(\theta={\rm arg}(z)\) are real numbers.

A one-dimensional wavefunction takes the general form

\[\label{e12.8} \psi(x,t) = A\,\cos(k\,x-\omega\,t+\varphi),\] where \(A\) is the wave amplitude, \(k\) the wavenumber, \(\omega\) the angular frequency, and \(\varphi\) the phase angle. Consider the complex wavefunction

\[\label{e12.10} \psi(x,t) = \psi_0\,{\rm e}^{\,{\rm i}\,(k\,x-\omega\,t)},\] where \(\psi_0\) is a complex constant. We can write \[\psi_0 = A\,{\rm e}^{\,{\rm i}\,\varphi},\] where \(A\) is the modulus, and \(\varphi\) the argument, of \(\psi_0\). Hence, we deduce that \[\begin{aligned} {\rm Re}\left[\psi_0\,{\rm e}^{\,{\rm i}\,(k\,x-\omega\,t)}\right] &= {\rm Re}\left[A\,{\rm e}^{\,{\rm i}\,\varphi}\,{\rm e}^{\,{\rm i}\,(k\,x-\omega\,t)}\right]={\rm Re}\left[A\,{\rm e}^{\,{\rm i}\,(k\,x-\omega\,t+\varphi)}\right]=A\,{\rm Re}\left[{\rm e}^{\,{\rm i}\,(k\,x-\omega\,t+\varphi)}\right].\end{aligned}\] Thus, it follows from Euler’s theorem, and Equation ( 2.3.4 ), that \[{\rm Re}\left[\psi_0\,{\rm e}^{\,{\rm i}\,(k\,x-\omega\,t)}\right] =A\,\cos(k\,x-\omega\,t+\varphi)=\psi(x,t).\] In other words, a general one-dimensional real wavefunction, ( 2.3.4 ), can be represented as the real part of a complex wavefunction of the form ( 2.3.5 ). For ease of notation, the “take the real part” aspect of the previous expression is usually omitted, and our general one-dimension wavefunction is simply written

\[\label{e12.13} \psi(x,t) = \psi_0\,{\rm e}^{\,{\rm i}\,(k\,x-\omega\,t)}.\] The main advantage of the complex representation, ( 2.3.8 ), over the more straightforward real representation, ( 2.3.4 ), is that the former enables us to combine the amplitude, \(A\), and the phase angle, \(\varphi\), of the wavefunction into a single complex amplitude, \(\psi_0\). Finally, the three-dimensional generalization of the previous expression is \[\psi({\bf r},t) = \psi_0\,{\rm e}^{\,{\rm i}\,({\bf k}\cdot{\bf r}-\omega\,t)},\] where \({\bf k}\) is the wavevector.

Contributors and Attributions

Richard Fitzpatrick (Professor of Physics, The University of Texas at Austin)

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  • Local transport

National Travel Attitudes Study: Wave 10

Attitudes and experiences relating to bus fare caps, concessionary travel, international travel and the European Entry Exit System (EES).

Applies to England

Ntas wave 10: concessionary bus travel and bus fare caps, ntas wave 10: international travel and european entry exit system, ntas wave 10: notes and methodology, ntas wave 10 table.

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In NTAS wave 10: 

among people aged 65 years and over, 81% own, or are in the process of acquiring, a concessionary bus pass

of users who were aware of the bus fare cap, 49% say they have made additional journeys on the bus that they would not have done without the £2 bus fare cap 

of users who were aware of the bus fare cap, 51% have taken the bus instead of other public transport modes because of the £2 bus fare cap 

of users of the bus in areas where the cap is in place, 37% say that if the £2 bus fare cap was extended to tickets other than adult single fares, they would take more bus journeys

of users of the bus in areas where the cap is in place, 53% say they would take the same amount of journeys if the cap were extended to other ticket types

of those who have travelled internationally for leisure in the past 12 months, 91% had done so via a plane

of those who travelled by plane, 32% experienced at least one event of transport disruption, compared to 33% of those who used a ferry or other boat, and 41% of those who used international rail

a total of 69% of respondents had not heard of the European Entry Exit System ( EES ) 

once EES is implemented, 65% say they will travel to Europe about the same over the next 2 years compared to now, with 15% saying they will travel less 

of those who say they will travel to Europe the same, or less, in the next 2 years compared to now due to EES , around two-thirds (67%) expressed concerns about queueing and additional document checking

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Guest Essay

How Big Tech Is Killing Innovation

An illustration of a man wearing business attire. He holds a phone in his left hand; his right pushes a vacuum cleaner. Beneath the vacuum are office cubicles; papers, workers and other items are getting sucked in.

By Mark Lemley and Matt Wansley

Mr. Lemley is a professor at Stanford Law School. Mr. Wansley is an associate professor at Cardozo School of Law.

Silicon Valley prides itself on disruption: Start-ups develop new technologies, upend existing markets and overtake incumbents. This cycle of creative destruction brought us the personal computer, the internet and the smartphone. But in recent years, a handful of incumbent tech companies have sustained their dominance. Why? We believe they have learned how to co-opt potentially disruptive start-ups before they can become competitive threats.

Just look at what’s happening to the leading companies in generative artificial intelligence.

DeepMind, one of the first prominent A.I. start-ups, was acquired by Google . OpenAI, founded as a nonprofit and counterweight to Google’s dominance, has raised $13 billion from Microsoft . Anthropic, a start-up founded by OpenAI engineers who grew wary of Microsoft’s influence, has raised $4 billion from Amazon and $2 billion from Google.

Last week, the news broke that the Federal Trade Commission was investigating Microsoft’s dealings with Inflection AI, a start-up founded by DeepMind engineers who used to work for Google. The government seems to be interested in whether Microsoft’s agreement to pay Inflection $650 million in a licensing deal — at the same time it was gutting the start-up by hiring away most of its engineering team — was an end run around antitrust laws.

Microsoft has defended its partnership with Inflection. But is the government right to be worried about these deals? We think so. In the short run, partnerships between A.I. start-ups and Big Tech give the start-ups the enormous sums of cash and hard-to-source chips they want. But in the long run, it is competition — not consolidation — that delivers technological progress.

Today’s tech giants were once small start-ups themselves. They built businesses by figuring out how to commercialize new technologies — Apple’s personal computer, Microsoft’s operating system, Amazon’s online marketplace, Google’s search engine and Facebook’s social network. These new technologies didn’t so much compete with incumbents as route around them, offering new ways of doing things that upended the expectations of the market.

But that pattern of start-ups innovating, growing and leapfrogging incumbents seems to have stopped. The tech giants are old. Each was founded more than 20 years ago — Apple and Microsoft in the 1970s, Amazon and Google in the 1990s, and Facebook in 2004. Why has no new competitor emerged to disrupt the market?

The answer isn’t that today’s tech giants are just better at innovating. The best available evidence — patent data — suggests that innovations are more likely to come from start-ups than established companies. And that’s also what economic theory would predict.

An incumbent with a large market share has less incentive to innovate because the new sales that an innovation would generate might cannibalize sales of its existing products. Talented engineers are less enthusiastic about stock in a large company that isn’t tied to the value of the project they are working on than stock in a start-up that might grow exponentially. And incumbent managers are rewarded for developing incremental improvements that satisfy their existing customers rather than disruptive innovations that might devalue the skills and relationships that give them power.

The tech giants have learned to stop the cycle of disruption . They invest in start-ups developing disruptive technologies, which gives them intelligence about competitive threats and the ability to influence the start-ups’ direction. Microsoft’s partnership with OpenAI illustrates the problem. In November, Satya Nadella, Microsoft’s chief executive, said that even if OpenAI disappeared suddenly, his customers would have no cause to worry, because “we have the people, we have the compute, we have the data, we have everything.”

Of course, incumbents have always stood to gain from choking off competition. Earlier tech companies like Intel and Cisco understood the value of acquiring start-ups with complementary products. What’s different today is that tech executives have learned that even start-ups outside their core markets can become dangerous competitive threats. And the sheer size of today’s tech giants gives them the cash to co-opt those threats. When Microsoft was on trial for antitrust violations in the late 1990s, it was valued in the tens of billions. Now it’s over 3 trillion.

In addition to their money, the tech giants can leverage access to their data and networks, rewarding start-ups that cooperate and punishing those that compete. Indeed, this is one of the government’s arguments in its new antitrust lawsuit against Apple . (Apple denied those claims and has asked for the case to be dismissed.) They can also use their connections in politics to encourage regulation that serves as a competitive moat.

Remember those Facebook ads advocating greater internet regulation ? Facebook wasn’t buying them for charity. Facebook’s proposals “consist largely of implementing requirements for content moderation systems that Facebook has previously put in place,” concludes tech-investigations site The Markup. That would give it a first-mover advantage over the competition.

When these tactics fail to steer a start-up away from competing, the tech giants can simply buy it. Mark Zuckerberg made this clear in an email to a colleague before Facebook bought Instagram. If start-ups like Instagram “grow to a large scale,” he wrote, “they could be very disruptive to us.”

The tech giants also cultivate repeat-player relationships with venture capitalists. Start-ups are risky investments, so for a venture fund to succeed, at least one of its portfolio companies must generate exponential returns. As initial public offerings have declined, venture capitalists have increasingly turned to acquisitions to deliver those returns. And the venture capitalists know that only a small number of companies can acquire a start-up at that kind of price, so they stay friendly with Big Tech in hopes of steering their start-ups to deals with incumbents. That’s why some prominent venture capitalists oppose stronger antitrust enforcement : It’s bad for business.

Co-option may seem harmless in the short run. Some partnerships between incumbents and start-ups are productive. And acquisitions give venture capitalists the returns they need to persuade their investors to commit more capital to the next wave of start-ups.

But co-option undermines technological progress. When one of the tech giants buys a start-up, it might shut down the start-up’s technology. Or it might divert the start-up’s people and assets to its own innovation needs. And even if it does neither, the structural obstacles that inhibit innovation at large incumbents could sap the creativity of the acquired start-up’s employees. A.I. looks like a classic disruptive technology. But as the disruptive start-ups that pioneered it get tied up with Big Tech one by one, it may become nothing more than a way of automating search engines.

The Biden administration can step in to begin to solve this problem.

Earlier this year, the F.T.C. announced it was investigating Big Tech’s deals with A.I. companies . That’s a promising start. But we need to change the rules that make co-option possible.

First, Congress should expand the law of “interlocking directorates” — which prohibits a company’s directors or officers from serving as directors or officers for its competitors — to prevent the tech giants from putting their employees on start-up boards. Second, the courts should penalize dominant companies that discriminate in access to their data or networks on the basis of whether the company is a potential competitor. Third, as Congress moves to regulate A.I., it should take care to write rules that don’t entrench incumbents.

Finally, the government should identify a list of potentially disruptive technologies — we’d start with A.I. and virtual reality — and announce that it will presumptively challenge any mergers between the tech giants and start-ups developing those technologies. That policy might make life difficult for venture capitalists who like to give talks about disruption and then get drinks with their friends in corporate development at Microsoft. But it would be good news for founders who want to sell products to customers, not start-ups to monopolies. And it would be good for consumers, who depend on competition but have spent too long without it.

Mark Lemley is a professor at Stanford Law School and co-founder of the legal analytics start-up Lex Machina. Matt Wansley is an associate professor at Cardozo School of Law and was general counsel of the automated driving start-up nuTonomy.

The Times is committed to publishing a diversity of letters to the editor. We’d like to hear what you think about this or any of our articles. Here are some tips . And here’s our email: [email protected] .

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The economic potential of generative AI: The next productivity frontier

travelling wave exponential

AI has permeated our lives incrementally, through everything from the tech powering our smartphones to autonomous-driving features on cars to the tools retailers use to surprise and delight consumers. As a result, its progress has been almost imperceptible. Clear milestones, such as when AlphaGo, an AI-based program developed by DeepMind, defeated a world champion Go player in 2016, were celebrated but then quickly faded from the public’s consciousness.

Generative AI applications such as ChatGPT, GitHub Copilot, Stable Diffusion, and others have captured the imagination of people around the world in a way AlphaGo did not, thanks to their broad utility—almost anyone can use them to communicate and create—and preternatural ability to have a conversation with a user. The latest generative AI applications can perform a range of routine tasks, such as the reorganization and classification of data. But it is their ability to write text, compose music, and create digital art that has garnered headlines and persuaded consumers and households to experiment on their own. As a result, a broader set of stakeholders are grappling with generative AI’s impact on business and society but without much context to help them make sense of it.

About the authors

This article is a collaborative effort by Michael Chui , Eric Hazan , Roger Roberts , Alex Singla , Kate Smaje , Alex Sukharevsky , Lareina Yee , and Rodney Zemmel , representing views from QuantumBlack, AI by McKinsey; McKinsey Digital; the McKinsey Technology Council; the McKinsey Global Institute; and McKinsey’s Growth, Marketing & Sales Practice.

The speed at which generative AI technology is developing isn’t making this task any easier. ChatGPT was released in November 2022. Four months later, OpenAI released a new large language model, or LLM, called GPT-4 with markedly improved capabilities. 1 “Introducing ChatGPT,” OpenAI, November 30, 2022; “GPT-4 is OpenAI’s most advanced system, producing safer and more useful responses,” OpenAI, accessed June 1, 2023. Similarly, by May 2023, Anthropic’s generative AI, Claude, was able to process 100,000 tokens of text, equal to about 75,000 words in a minute—the length of the average novel—compared with roughly 9,000 tokens when it was introduced in March 2023. 2 “Introducing Claude,” Anthropic PBC, March 14, 2023; “Introducing 100K Context Windows,” Anthropic PBC, May 11, 2023. And in May 2023, Google announced several new features powered by generative AI, including Search Generative Experience and a new LLM called PaLM 2 that will power its Bard chatbot, among other Google products. 3 Emma Roth, “The nine biggest announcements from Google I/O 2023,” The Verge , May 10, 2023.

To grasp what lies ahead requires an understanding of the breakthroughs that have enabled the rise of generative AI, which were decades in the making. For the purposes of this report, we define generative AI as applications typically built using foundation models. These models contain expansive artificial neural networks inspired by the billions of neurons connected in the human brain. Foundation models are part of what is called deep learning, a term that alludes to the many deep layers within neural networks. Deep learning has powered many of the recent advances in AI, but the foundation models powering generative AI applications are a step-change evolution within deep learning. Unlike previous deep learning models, they can process extremely large and varied sets of unstructured data and perform more than one task.

Never just tech

Creating value beyond the hype

Let’s deliver on the promise of technology from strategy to scale.

Foundation models have enabled new capabilities and vastly improved existing ones across a broad range of modalities, including images, video, audio, and computer code. AI trained on these models can perform several functions; it can classify, edit, summarize, answer questions, and draft new content, among other tasks.

All of us are at the beginning of a journey to understand generative AI’s power, reach, and capabilities. This research is the latest in our efforts to assess the impact of this new era of AI. It suggests that generative AI is poised to transform roles and boost performance across functions such as sales and marketing, customer operations, and software development. In the process, it could unlock trillions of dollars in value across sectors from banking to life sciences. The following sections share our initial findings.

For the full version of this report, download the PDF .

Key insights

Generative AI’s impact on productivity could add trillions of dollars in value to the global economy. Our latest research estimates that generative AI could add the equivalent of $2.6 trillion to $4.4 trillion annually across the 63 use cases we analyzed—by comparison, the United Kingdom’s entire GDP in 2021 was $3.1 trillion. This would increase the impact of all artificial intelligence by 15 to 40 percent. This estimate would roughly double if we include the impact of embedding generative AI into software that is currently used for other tasks beyond those use cases.

About 75 percent of the value that generative AI use cases could deliver falls across four areas: Customer operations, marketing and sales, software engineering, and R&D. Across 16 business functions, we examined 63 use cases in which the technology can address specific business challenges in ways that produce one or more measurable outcomes. Examples include generative AI’s ability to support interactions with customers, generate creative content for marketing and sales, and draft computer code based on natural-language prompts, among many other tasks.

Generative AI will have a significant impact across all industry sectors. Banking, high tech, and life sciences are among the industries that could see the biggest impact as a percentage of their revenues from generative AI. Across the banking industry, for example, the technology could deliver value equal to an additional $200 billion to $340 billion annually if the use cases were fully implemented. In retail and consumer packaged goods, the potential impact is also significant at $400 billion to $660 billion a year.

Generative AI has the potential to change the anatomy of work, augmenting the capabilities of individual workers by automating some of their individual activities. Current generative AI and other technologies have the potential to automate work activities that absorb 60 to 70 percent of employees’ time today. In contrast, we previously estimated that technology has the potential to automate half of the time employees spend working. 4 “ Harnessing automation for a future that works ,” McKinsey Global Institute, January 12, 2017. The acceleration in the potential for technical automation is largely due to generative AI’s increased ability to understand natural language, which is required for work activities that account for 25 percent of total work time. Thus, generative AI has more impact on knowledge work associated with occupations that have higher wages and educational requirements than on other types of work.

The pace of workforce transformation is likely to accelerate, given increases in the potential for technical automation. Our updated adoption scenarios, including technology development, economic feasibility, and diffusion timelines, lead to estimates that half of today’s work activities could be automated between 2030 and 2060, with a midpoint in 2045, or roughly a decade earlier than in our previous estimates.

Generative AI can substantially increase labor productivity across the economy, but that will require investments to support workers as they shift work activities or change jobs. Generative AI could enable labor productivity growth of 0.1 to 0.6 percent annually through 2040, depending on the rate of technology adoption and redeployment of worker time into other activities. Combining generative AI with all other technologies, work automation could add 0.5 to 3.4 percentage points annually to productivity growth. However, workers will need support in learning new skills, and some will change occupations. If worker transitions and other risks can be managed, generative AI could contribute substantively to economic growth and support a more sustainable, inclusive world.

The era of generative AI is just beginning. Excitement over this technology is palpable, and early pilots are compelling. But a full realization of the technology’s benefits will take time, and leaders in business and society still have considerable challenges to address. These include managing the risks inherent in generative AI, determining what new skills and capabilities the workforce will need, and rethinking core business processes such as retraining and developing new skills.

Where business value lies

Generative AI is a step change in the evolution of artificial intelligence. As companies rush to adapt and implement it, understanding the technology’s potential to deliver value to the economy and society at large will help shape critical decisions. We have used two complementary lenses to determine where generative AI, with its current capabilities, could deliver the biggest value and how big that value could be (Exhibit 1).

The first lens scans use cases for generative AI that organizations could adopt. We define a “use case” as a targeted application of generative AI to a specific business challenge, resulting in one or more measurable outcomes. For example, a use case in marketing is the application of generative AI to generate creative content such as personalized emails, the measurable outcomes of which potentially include reductions in the cost of generating such content and increases in revenue from the enhanced effectiveness of higher-quality content at scale. We identified 63 generative AI use cases spanning 16 business functions that could deliver total value in the range of $2.6 trillion to $4.4 trillion in economic benefits annually when applied across industries.

That would add 15 to 40 percent to the $11 trillion to $17.7 trillion of economic value that we now estimate nongenerative artificial intelligence and analytics could unlock. (Our previous estimate from 2017 was that AI could deliver $9.5 trillion to $15.4 trillion in economic value.)

Our second lens complements the first by analyzing generative AI’s potential impact on the work activities required in some 850 occupations. We modeled scenarios to estimate when generative AI could perform each of more than 2,100 “detailed work activities”—such as “communicating with others about operational plans or activities”—that make up those occupations across the world economy. This enables us to estimate how the current capabilities of generative AI could affect labor productivity across all work currently done by the global workforce.

Some of this impact will overlap with cost reductions in the use case analysis described above, which we assume are the result of improved labor productivity. Netting out this overlap, the total economic benefits of generative AI —including the major use cases we explored and the myriad increases in productivity that are likely to materialize when the technology is applied across knowledge workers’ activities—amounts to $6.1 trillion to $7.9 trillion annually (Exhibit 2).

How we estimated the value potential of generative AI use cases

To assess the potential value of generative AI, we updated a proprietary McKinsey database of potential AI use cases and drew on the experience of more than 100 experts in industries and their business functions. 1 ” Notes from the AI frontier: Applications and value of deep learning ,” McKinsey Global Institute, April 17, 2018.

Our updates examined use cases of generative AI—specifically, how generative AI techniques (primarily transformer-based neural networks) can be used to solve problems not well addressed by previous technologies.

We analyzed only use cases for which generative AI could deliver a significant improvement in the outputs that drive key value. In particular, our estimates of the primary value the technology could unlock do not include use cases for which the sole benefit would be its ability to use natural language. For example, natural-language capabilities would be the key driver of value in a customer service use case but not in a use case optimizing a logistics network, where value primarily arises from quantitative analysis.

We then estimated the potential annual value of these generative AI use cases if they were adopted across the entire economy. For use cases aimed at increasing revenue, such as some of those in sales and marketing, we estimated the economy-wide value generative AI could deliver by increasing the productivity of sales and marketing expenditures.

Our estimates are based on the structure of the global economy in 2022 and do not consider the value generative AI could create if it produced entirely new product or service categories.

While generative AI is an exciting and rapidly advancing technology, the other applications of AI discussed in our previous report continue to account for the majority of the overall potential value of AI. Traditional advanced-analytics and machine learning algorithms are highly effective at performing numerical and optimization tasks such as predictive modeling, and they continue to find new applications in a wide range of industries. However, as generative AI continues to develop and mature, it has the potential to open wholly new frontiers in creativity and innovation. It has already expanded the possibilities of what AI overall can achieve (see sidebar “How we estimated the value potential of generative AI use cases”).

In this section, we highlight the value potential of generative AI across business functions.

Generative AI could have an impact on most business functions; however, a few stand out when measured by the technology’s impact as a share of functional cost (Exhibit 3). Our analysis of 16 business functions identified just four—customer operations, marketing and sales, software engineering, and research and development—that could account for approximately 75 percent of the total annual value from generative AI use cases.

Notably, the potential value of using generative AI for several functions that were prominent in our previous sizing of AI use cases, including manufacturing and supply chain functions, is now much lower. 5 Pitchbook. This is largely explained by the nature of generative AI use cases, which exclude most of the numerical and optimization applications that were the main value drivers for previous applications of AI.

In addition to the potential value generative AI can deliver in function-specific use cases, the technology could drive value across an entire organization by revolutionizing internal knowledge management systems. Generative AI’s impressive command of natural-language processing can help employees retrieve stored internal knowledge by formulating queries in the same way they might ask a human a question and engage in continuing dialogue. This could empower teams to quickly access relevant information, enabling them to rapidly make better-informed decisions and develop effective strategies.

In 2012, the McKinsey Global Institute (MGI) estimated that knowledge workers spent about a fifth of their time, or one day each work week, searching for and gathering information. If generative AI could take on such tasks, increasing the efficiency and effectiveness of the workers doing them, the benefits would be huge. Such virtual expertise could rapidly “read” vast libraries of corporate information stored in natural language and quickly scan source material in dialogue with a human who helps fine-tune and tailor its research, a more scalable solution than hiring a team of human experts for the task.

In other cases, generative AI can drive value by working in partnership with workers, augmenting their work in ways that accelerate their productivity. Its ability to rapidly digest mountains of data and draw conclusions from it enables the technology to offer insights and options that can dramatically enhance knowledge work. This can significantly speed up the process of developing a product and allow employees to devote more time to higher-impact tasks.

Following are four examples of how generative AI could produce operational benefits in a handful of use cases across the business functions that could deliver a majority of the potential value we identified in our analysis of 63 generative AI use cases. In the first two examples, it serves as a virtual expert, while in the following two, it lends a hand as a virtual collaborator.

Customer operations: Improving customer and agent experiences

Generative AI has the potential to revolutionize the entire customer operations function, improving the customer experience and agent productivity through digital self-service and enhancing and augmenting agent skills. The technology has already gained traction in customer service because of its ability to automate interactions with customers using natural language. Research found that at one company with 5,000 customer service agents, the application of generative AI increased issue resolution by 14 percent an hour and reduced the time spent handling an issue by 9 percent. 1 Erik Brynjolfsson, Danielle Li, and Lindsey R. Raymond, Generative AI at work , National Bureau of Economic Research working paper number 31161, April 2023. It also reduced agent attrition and requests to speak to a manager by 25 percent. Crucially, productivity and quality of service improved most among less-experienced agents, while the AI assistant did not increase—and sometimes decreased—the productivity and quality metrics of more highly skilled agents. This is because AI assistance helped less-experienced agents communicate using techniques similar to those of their higher-skilled counterparts.

The following are examples of the operational improvements generative AI can have for specific use cases:

  • Customer self-service. Generative AI–fueled chatbots can give immediate and personalized responses to complex customer inquiries regardless of the language or location of the customer. By improving the quality and effectiveness of interactions via automated channels, generative AI could automate responses to a higher percentage of customer inquiries, enabling customer care teams to take on inquiries that can only be resolved by a human agent. Our research found that roughly half of customer contacts made by banking, telecommunications, and utilities companies in North America are already handled by machines, including but not exclusively AI. We estimate that generative AI could further reduce the volume of human-serviced contacts by up to 50 percent, depending on a company’s existing level of automation.
  • Resolution during initial contact. Generative AI can instantly retrieve data a company has on a specific customer, which can help a human customer service representative more successfully answer questions and resolve issues during an initial interaction.
  • Reduced response time. Generative AI can cut the time a human sales representative spends responding to a customer by providing assistance in real time and recommending next steps.
  • Increased sales. Because of its ability to rapidly process data on customers and their browsing histories, the technology can identify product suggestions and deals tailored to customer preferences. Additionally, generative AI can enhance quality assurance and coaching by gathering insights from customer conversations, determining what could be done better, and coaching agents.

We estimate that applying generative AI to customer care functions could increase productivity at a value ranging from 30 to 45 percent of current function costs.

Our analysis captures only the direct impact generative AI might have on the productivity of customer operations. It does not account for potential knock-on effects the technology may have on customer satisfaction and retention arising from an improved experience, including better understanding of the customer’s context that can assist human agents in providing more personalized help and recommendations.

Marketing and sales: Boosting personalization, content creation, and sales productivity

Generative AI has taken hold rapidly in marketing and sales functions, in which text-based communications and personalization at scale are driving forces. The technology can create personalized messages tailored to individual customer interests, preferences, and behaviors, as well as do tasks such as producing first drafts of brand advertising, headlines, slogans, social media posts, and product descriptions.

Introducing generative AI to marketing functions requires careful consideration. For one thing, mathematical models trained on publicly available data without sufficient safeguards against plagiarism, copyright violations, and branding recognition risks infringing on intellectual property rights. A virtual try-on application may produce biased representations of certain demographics because of limited or biased training data. Thus, significant human oversight is required for conceptual and strategic thinking specific to each company’s needs.

Potential operational benefits from using generative AI for marketing include the following:

  • Efficient and effective content creation. Generative AI could significantly reduce the time required for ideation and content drafting, saving valuable time and effort. It can also facilitate consistency across different pieces of content, ensuring a uniform brand voice, writing style, and format. Team members can collaborate via generative AI, which can integrate their ideas into a single cohesive piece. This would allow teams to significantly enhance personalization of marketing messages aimed at different customer segments, geographies, and demographics. Mass email campaigns can be instantly translated into as many languages as needed, with different imagery and messaging depending on the audience. Generative AI’s ability to produce content with varying specifications could increase customer value, attraction, conversion, and retention over a lifetime and at a scale beyond what is currently possible through traditional techniques.
  • Enhanced use of data. Generative AI could help marketing functions overcome the challenges of unstructured, inconsistent, and disconnected data—for example, from different databases—by interpreting abstract data sources such as text, image, and varying structures. It can help marketers better use data such as territory performance, synthesized customer feedback, and customer behavior to generate data-informed marketing strategies such as targeted customer profiles and channel recommendations. Such tools could identify and synthesize trends, key drivers, and market and product opportunities from unstructured data such as social media, news, academic research, and customer feedback.
  • SEO optimization. Generative AI can help marketers achieve higher conversion and lower cost through search engine optimization (SEO) for marketing and sales technical components such as page titles, image tags, and URLs. It can synthesize key SEO tokens, support specialists in SEO digital content creation, and distribute targeted content to customers.
  • Product discovery and search personalization. With generative AI, product discovery and search can be personalized with multimodal inputs from text, images, and speech, and a deep understanding of customer profiles. For example, technology can leverage individual user preferences, behavior, and purchase history to help customers discover the most relevant products and generate personalized product descriptions. This would allow CPG, travel, and retail companies to improve their e-commerce sales by achieving higher website conversion rates.

We estimate that generative AI could increase the productivity of the marketing function with a value between 5 and 15 percent of total marketing spending.

Our analysis of the potential use of generative AI in marketing doesn’t account for knock-on effects beyond the direct impacts on productivity. Generative AI–enabled synthesis could provide higher-quality data insights, leading to new ideas for marketing campaigns and better-targeted customer segments. Marketing functions could shift resources to producing higher-quality content for owned channels, potentially reducing spending on external channels and agencies.

Generative AI could also change the way both B2B and B2C companies approach sales. The following are two use cases for sales:

  • Increase probability of sale. Generative AI could identify and prioritize sales leads by creating comprehensive consumer profiles from structured and unstructured data and suggesting actions to staff to improve client engagement at every point of contact. For example, generative AI could provide better information about client preferences, potentially improving close rates.
  • Improve lead development. Generative AI could help sales representatives nurture leads by synthesizing relevant product sales information and customer profiles and creating discussion scripts to facilitate customer conversation, including up- and cross-selling talking points. It could also automate sales follow-ups and passively nurture leads until clients are ready for direct interaction with a human sales agent.

Our analysis suggests that implementing generative AI could increase sales productivity by approximately 3 to 5 percent of current global sales expenditures.

This analysis may not fully account for additional revenue that generative AI could bring to sales functions. For instance, generative AI’s ability to identify leads and follow-up capabilities could uncover new leads and facilitate more effective outreach that would bring in additional revenue. Also, the time saved by sales representatives due to generative AI’s capabilities could be invested in higher-quality customer interactions, resulting in increased sales success.

Software engineering: Speeding developer work as a coding assistant

Treating computer languages as just another language opens new possibilities for software engineering. Software engineers can use generative AI in pair programming and to do augmented coding and train LLMs to develop applications that generate code when given a natural-language prompt describing what that code should do.

Software engineering is a significant function in most companies, and it continues to grow as all large companies, not just tech titans, embed software in a wide array of products and services. For example, much of the value of new vehicles comes from digital features such as adaptive cruise control, parking assistance, and IoT connectivity.

According to our analysis, the direct impact of AI on the productivity of software engineering could range from 20 to 45 percent of current annual spending on the function. This value would arise primarily from reducing time spent on certain activities, such as generating initial code drafts, code correction and refactoring, root-cause analysis, and generating new system designs. By accelerating the coding process, generative AI could push the skill sets and capabilities needed in software engineering toward code and architecture design. One study found that software developers using Microsoft’s GitHub Copilot completed tasks 56 percent faster than those not using the tool. 1 Peter Cihon et al., The impact of AI on developer productivity: Evidence from GitHub Copilot , Cornell University arXiv software engineering working paper, arXiv:2302.06590, February 13, 2023. An internal McKinsey empirical study of software engineering teams found those who were trained to use generative AI tools rapidly reduced the time needed to generate and refactor code—and engineers also reported a better work experience, citing improvements in happiness, flow, and fulfillment.

Our analysis did not account for the increase in application quality and the resulting boost in productivity that generative AI could bring by improving code or enhancing IT architecture—which can improve productivity across the IT value chain. However, the quality of IT architecture still largely depends on software architects, rather than on initial drafts that generative AI’s current capabilities allow it to produce.

Large technology companies are already selling generative AI for software engineering, including GitHub Copilot, which is now integrated with OpenAI’s GPT-4, and Replit, used by more than 20 million coders. 2 Michael Nuñez, “Google and Replit join forces to challenge Microsoft in coding tools,” VentureBeat, March 28, 2023.

Product R&D: Reducing research and design time, improving simulation and testing

Generative AI’s potential in R&D is perhaps less well recognized than its potential in other business functions. Still, our research indicates the technology could deliver productivity with a value ranging from 10 to 15 percent of overall R&D costs.

For example, the life sciences and chemical industries have begun using generative AI foundation models in their R&D for what is known as generative design. Foundation models can generate candidate molecules, accelerating the process of developing new drugs and materials. Entos, a biotech pharmaceutical company, has paired generative AI with automated synthetic development tools to design small-molecule therapeutics. But the same principles can be applied to the design of many other products, including larger-scale physical products and electrical circuits, among others.

While other generative design techniques have already unlocked some of the potential to apply AI in R&D, their cost and data requirements, such as the use of “traditional” machine learning, can limit their application. Pretrained foundation models that underpin generative AI, or models that have been enhanced with fine-tuning, have much broader areas of application than models optimized for a single task. They can therefore accelerate time to market and broaden the types of products to which generative design can be applied. For now, however, foundation models lack the capabilities to help design products across all industries.

In addition to the productivity gains that result from being able to quickly produce candidate designs, generative design can also enable improvements in the designs themselves, as in the following examples of the operational improvements generative AI could bring:

  • Enhanced design. Generative AI can help product designers reduce costs by selecting and using materials more efficiently. It can also optimize designs for manufacturing, which can lead to cost reductions in logistics and production.
  • Improved product testing and quality. Using generative AI in generative design can produce a higher-quality product, resulting in increased attractiveness and market appeal. Generative AI can help to reduce testing time of complex systems and accelerate trial phases involving customer testing through its ability to draft scenarios and profile testing candidates.

We also identified a new R&D use case for nongenerative AI: deep learning surrogates, the use of which has grown since our earlier research, can be paired with generative AI to produce even greater benefits. To be sure, integration will require the development of specific solutions, but the value could be significant because deep learning surrogates have the potential to accelerate the testing of designs proposed by generative AI.

While we have estimated the potential direct impacts of generative AI on the R&D function, we did not attempt to estimate the technology’s potential to create entirely novel product categories. These are the types of innovations that can produce step changes not only in the performance of individual companies but in economic growth overall.

Industry impacts

Across the 63 use cases we analyzed, generative AI has the potential to generate $2.6 trillion to $4.4 trillion in value across industries. Its precise impact will depend on a variety of factors, such as the mix and importance of different functions, as well as the scale of an industry’s revenue (Exhibit 4).

For example, our analysis estimates generative AI could contribute roughly $310 billion in additional value for the retail industry (including auto dealerships) by boosting performance in functions such as marketing and customer interactions. By comparison, the bulk of potential value in high tech comes from generative AI’s ability to increase the speed and efficiency of software development (Exhibit 5).

In the banking industry, generative AI has the potential to improve on efficiencies already delivered by artificial intelligence by taking on lower-value tasks in risk management, such as required reporting, monitoring regulatory developments, and collecting data. In the life sciences industry, generative AI is poised to make significant contributions to drug discovery and development.

We share our detailed analysis of these industries below.

Generative AI supports key value drivers in retail and consumer packaged goods

The technology could generate value for the retail and consumer packaged goods (CPG) industry by increasing productivity by 1.2 to 2.0 percent of annual revenues, or an additional $400 billion to $660 billion. 1 Vehicular retail is included as part of our overall retail analysis. To streamline processes, generative AI could automate key functions such as customer service, marketing and sales, and inventory and supply chain management. Technology has played an essential role in the retail and CPG industries for decades. Traditional AI and advanced analytics solutions have helped companies manage vast pools of data across large numbers of SKUs, expansive supply chain and warehousing networks, and complex product categories such as consumables. In addition, the industries are heavily customer facing, which offers opportunities for generative AI to complement previously existing artificial intelligence. For example, generative AI’s ability to personalize offerings could optimize marketing and sales activities already handled by existing AI solutions. Similarly, generative AI tools excel at data management and could support existing AI-driven pricing tools. Applying generative AI to such activities could be a step toward integrating applications across a full enterprise.

Generative AI at work in retail and CPG

Reinvention of the customer interaction pattern.

Consumers increasingly seek customization in everything from clothing and cosmetics to curated shopping experiences, personalized outreach, and food—and generative AI can improve that experience. Generative AI can aggregate market data to test concepts, ideas, and models. Stitch Fix, which uses algorithms to suggest style choices to its customers, has experimented with DALL·E to visualize products based on customer preferences regarding color, fabric, and style. Using text-to-image generation, the company’s stylists can visualize an article of clothing based on a consumer’s preferences and then identify a similar article among Stitch Fix’s inventory.

Retailers can create applications that give shoppers a next-generation experience, creating a significant competitive advantage in an era when customers expect to have a single natural-language interface help them select products. For example, generative AI can improve the process of choosing and ordering ingredients for a meal or preparing food—imagine a chatbot that could pull up the most popular tips from the comments attached to a recipe. There is also a big opportunity to enhance customer value management by delivering personalized marketing campaigns through a chatbot. Such applications can have human-like conversations about products in ways that can increase customer satisfaction, traffic, and brand loyalty. Generative AI offers retailers and CPG companies many opportunities to cross-sell and upsell, collect insights to improve product offerings, and increase their customer base, revenue opportunities, and overall marketing ROI.

Accelerating the creation of value in key areas

Generative AI tools can facilitate copy writing for marketing and sales, help brainstorm creative marketing ideas, expedite consumer research, and accelerate content analysis and creation. The potential improvement in writing and visuals can increase awareness and improve sales conversion rates.

Rapid resolution and enhanced insights in customer care

The growth of e-commerce also elevates the importance of effective consumer interactions. Retailers can combine existing AI tools with generative AI to enhance the capabilities of chatbots, enabling them to better mimic the interaction style of human agents—for example, by responding directly to a customer’s query, tracking or canceling an order, offering discounts, and upselling. Automating repetitive tasks allows human agents to devote more time to handling complicated customer problems and obtaining contextual information.

Disruptive and creative innovation

Generative AI tools can enhance the process of developing new versions of products by digitally creating new designs rapidly. A designer can generate packaging designs from scratch or generate variations on an existing design. This technology is developing rapidly and has the potential to add text-to-video generation.

Factors for retail and CPG organizations to consider

As retail and CPG executives explore how to integrate generative AI in their operations, they should keep in mind several factors that could affect their ability to capture value from the technology:

  • External inference. Generative AI has increased the need to understand whether generated content is based on fact or inference, requiring a new level of quality control.
  • Adversarial attacks. Foundation models are a prime target for attack by hackers and other bad actors, increasing the variety of potential security vulnerabilities and privacy risks.

To address these concerns, retail and CPG companies will need to strategically keep humans in the loop and ensure security and privacy are top considerations for any implementation. Companies will need to institute new quality checks for processes previously handled by humans, such as emails written by customer reps, and perform more-detailed quality checks on AI-assisted processes such as product design.

Why banks could realize significant value

Generative AI could have a significant impact on the banking industry , generating value from increased productivity of 2.8 to 4.7 percent of the industry’s annual revenues, or an additional $200 billion to $340 billion. On top of that impact, the use of generative AI tools could also enhance customer satisfaction, improve decision making and employee experience, and decrease risks through better monitoring of fraud and risk.

Banking, a knowledge and technology-enabled industry, has already benefited significantly from previously existing applications of artificial intelligence in areas such as marketing and customer operations. 1 “ Building the AI bank of the future ,” McKinsey, May 2021. Generative AI applications could deliver additional benefits, especially because text modalities are prevalent in areas such as regulations and programming language, and the industry is customer facing, with many B2C and small-business customers. 2 McKinsey’s Global Banking Annual Review , December 1, 2022.

Several characteristics position the industry for the integration of generative AI applications:

  • Sustained digitization efforts along with legacy IT systems. Banks have been investing in technology for decades, accumulating a significant amount of technical debt along with a siloed and complex IT architecture. 3 Akhil Babbar, Raghavan Janardhanan, Remy Paternoster, and Henning Soller, “ Why most digital banking transformations fail—and how to flip the odds ,” McKinsey, April 11, 2023.
  • Large customer-facing workforces. Banking relies on a large number of service representatives such as call-center agents and wealth management financial advisers.
  • A stringent regulatory environment. As a heavily regulated industry, banking has a substantial number of risk, compliance, and legal needs.
  • White-collar industry. Generative AI’s impact could span the organization, assisting all employees in writing emails, creating business presentations, and other tasks.

Generative AI at work in banking

Banks have started to grasp the potential of generative AI in their front lines and in their software activities. Early adopters are harnessing solutions such as ChatGPT as well as industry-specific solutions, primarily for software and knowledge applications. Three uses demonstrate its value potential to the industry.

A virtual expert to augment employee performance

A generative AI bot trained on proprietary knowledge such as policies, research, and customer interaction could provide always-on, deep technical support. Today, frontline spending is dedicated mostly to validating offers and interacting with clients, but giving frontline workers access to data as well could improve the customer experience. The technology could also monitor industries and clients and send alerts on semantic queries from public sources. For example, Morgan Stanley is building an AI assistant using GPT-4, with the aim of helping tens of thousands of wealth managers quickly find and synthesize answers from a massive internal knowledge base. 4 Hugh Son, “Morgan Stanley is testing an OpenAI-powered chatbot for its 16,000 financial advisors,” CNBC, March 14, 2023. The model combines search and content creation so wealth managers can find and tailor information for any client at any moment.

One European bank has leveraged generative AI to develop an environmental, social, and governance (ESG) virtual expert by synthesizing and extracting from long documents with unstructured information. The model answers complex questions based on a prompt, identifying the source of each answer and extracting information from pictures and tables.

Generative AI could reduce the significant costs associated with back-office operations. Such customer-facing chatbots could assess user requests and select the best service expert to address them based on characteristics such as topic, level of difficulty, and type of customer. Through generative AI assistants, service professionals could rapidly access all relevant information such as product guides and policies to instantaneously address customer requests.

Code acceleration to reduce tech debt and deliver software faster

Generative AI tools are useful for software development in four broad categories. First, they can draft code based on context via input code or natural language, helping developers code more quickly and with reduced friction while enabling automatic translations and no- and low-code tools. Second, such tools can automatically generate, prioritize, run, and review different code tests, accelerating testing and increasing coverage and effectiveness. Third, generative AI’s natural-language translation capabilities can optimize the integration and migration of legacy frameworks. Last, the tools can review code to identify defects and inefficiencies in computing. The result is more robust, effective code.

Production of tailored content at scale

Generative AI tools can draw on existing documents and data sets to substantially streamline content generation. These tools can create personalized marketing and sales content tailored to specific client profiles and histories as well as a multitude of alternatives for A/B testing. In addition, generative AI could automatically produce model documentation, identify missing documentation, and scan relevant regulatory updates to create alerts for relevant shifts.

Factors for banks to consider

When exploring how to integrate generative AI into operations, banks can be mindful of a number of factors:

  • The level of regulation for different processes. These vary from unregulated processes such as customer service to heavily regulated processes such as credit risk scoring.
  • Type of end user. End users vary widely in their expectations and familiarity with generative AI—for example, employees compared with high-net-worth clients.
  • Intended level of work automation. AI agents integrated through APIs could act nearly autonomously or as copilots, giving real-time suggestions to agents during customer interactions.
  • Data constraints. While public data such as annual reports could be made widely available, there would need to be limits on identifiable details for customers and other internal data.

Pharmaceuticals and medical products could see benefits across the entire value chain

Our analysis finds that generative AI could have a significant impact on the pharmaceutical and medical-product industries—from 2.6 to 4.5 percent of annual revenues across the pharmaceutical and medical-product industries, or $60 billion to $110 billion annually. This big potential reflects the resource-intensive process of discovering new drug compounds. Pharma companies typically spend approximately 20 percent of revenues on R&D, 1 Research and development in the pharmaceutical industry , Congressional Budget Office, April 2021. and the development of a new drug takes an average of ten to 15 years. With this level of spending and timeline, improving the speed and quality of R&D can generate substantial value. For example, lead identification—a step in the drug discovery process in which researchers identify a molecule that would best address the target for a potential new drug—can take several months even with “traditional” deep learning techniques. Foundation models and generative AI can enable organizations to complete this step in a matter of weeks.

Generative AI at work in pharmaceuticals and medical products

Drug discovery involves narrowing the universe of possible compounds to those that could effectively treat specific conditions. Generative AI’s ability to process massive amounts of data and model options can accelerate output across several use cases:

Improve automation of preliminary screening

In the lead identification stage of drug development, scientists can use foundation models to automate the preliminary screening of chemicals in the search for those that will produce specific effects on drug targets. To start, thousands of cell cultures are tested and paired with images of the corresponding experiment. Using an off-the-shelf foundation model, researchers can cluster similar images more precisely than they can with traditional models, enabling them to select the most promising chemicals for further analysis during lead optimization.

Enhance indication finding

An important phase of drug discovery involves the identification and prioritization of new indications—that is, diseases, symptoms, or circumstances that justify the use of a specific medication or other treatment, such as a test, procedure, or surgery. Possible indications for a given drug are based on a patient group’s clinical history and medical records, and they are then prioritized based on their similarities to established and evidence-backed indications.

Researchers start by mapping the patient cohort’s clinical events and medical histories—including potential diagnoses, prescribed medications, and performed procedures—from real-world data. Using foundation models, researchers can quantify clinical events, establish relationships, and measure the similarity between the patient cohort and evidence-backed indications. The result is a short list of indications that have a better probability of success in clinical trials because they can be more accurately matched to appropriate patient groups.

Pharma companies that have used this approach have reported high success rates in clinical trials for the top five indications recommended by a foundation model for a tested drug. This success has allowed these drugs to progress smoothly into Phase 3 trials, significantly accelerating the drug development process.

Factors for pharmaceuticals and medical products organizations to consider

Before integrating generative AI into operations, pharma executives should be aware of some factors that could limit their ability to capture its benefits:

  • The need for a human in the loop. Companies may need to implement new quality checks on processes that shift from humans to generative AI, such as representative-generated emails, or more detailed quality checks on AI-assisted processes, such as drug discovery. The increasing need to verify whether generated content is based on fact or inference elevates the need for a new level of quality control.
  • Explainability. A lack of transparency into the origins of generated content and traceability of root data could make it difficult to update models and scan them for potential risks; for instance, a generative AI solution for synthesizing scientific literature may not be able to point to the specific articles or quotes that led it to infer that a new treatment is very popular among physicians. The technology can also “hallucinate,” or generate responses that are obviously incorrect or inappropriate for the context. Systems need to be designed to point to specific articles or data sources, and then do human-in-the-loop checking.
  • Privacy considerations. Generative AI’s use of clinical images and medical records could increase the risk that protected health information will leak, potentially violating regulations that require pharma companies to protect patient privacy.

Work and productivity implications

Technology has been changing the anatomy of work for decades. Over the years, machines have given human workers various “superpowers”; for instance, industrial-age machines enabled workers to accomplish physical tasks beyond the capabilities of their own bodies. More recently, computers have enabled knowledge workers to perform calculations that would have taken years to do manually.

These examples illustrate how technology can augment work through the automation of individual activities that workers would have otherwise had to do themselves. At a conceptual level, the application of generative AI may follow the same pattern in the modern workplace, although as we show later in this chapter, the types of activities that generative AI could affect, and the types of occupations with activities that could change, will likely be different as a result of this technology than for older technologies.

The McKinsey Global Institute began analyzing the impact of technological automation of work activities and modeling scenarios of adoption in 2017. At that time, we estimated that workers spent half of their time on activities that had the potential to be automated by adapting technology that existed at that time, or what we call technical automation potential. We also modeled a range of potential scenarios for the pace at which these technologies could be adopted and affect work activities throughout the global economy.

Technology adoption at scale does not occur overnight. The potential of technological capabilities in a lab does not necessarily mean they can be immediately integrated into a solution that automates a specific work activity—developing such solutions takes time. Even when such a solution is developed, it might not be economically feasible to use if its costs exceed those of human labor. Additionally, even if economic incentives for deployment exist, it takes time for adoption to spread across the global economy. Hence, our adoption scenarios, which consider these factors together with the technical automation potential, provide a sense of the pace and scale at which workers’ activities could shift over time.

About the research

This analysis builds on the methodology we established in 2017. We began by examining the US Bureau of Labor Statistics O*Net breakdown of about 850 occupations into roughly 2,100 detailed work activities. For each of these activities, we scored the level of capability necessary to successfully perform the activity against a set of 18 capabilities that have the potential for automation.

We also surveyed experts in the automation of each of these capabilities to estimate automation technologies’ current performance level against each of these capabilities, as well as how the technology’s performance might advance over time. Specifically, this year, we updated our assessments of technology’s performance in cognitive, language, and social and emotional capabilities based on a survey of generative AI experts.

Based on these assessments of the technical automation potential of each detailed work activity at each point in time, we modeled potential scenarios for the adoption of work automation around the world. First, we estimated a range of time to implement a solution that could automate each specific detailed work activity, once all the capability requirements were met by the state of technology development. Second, we estimated a range of potential costs for this technology when it is first introduced, and then declining over time, based on historical precedents. We modeled the beginning of adoption for a specific detailed work activity in a particular occupation in a country (for 47 countries, accounting for more than 80 percent of the global workforce) when the cost of the automation technology reaches parity with the cost of human labor in that occupation.

Based on a historical analysis of various technologies, we modeled a range of adoption timelines from eight to 27 years between the beginning of adoption and its plateau, using sigmoidal curves (S-curves). This range implicitly accounts for the many factors that could affect the pace at which adoption occurs, including regulation, levels of investment, and management decision making within firms.

The modeled scenarios create a time range for the potential pace of automating current work activities. The “earliest” scenario flexes all parameters to the extremes of plausible assumptions, resulting in faster automation development and adoption, and the “latest” scenario flexes all parameters in the opposite direction. The reality is likely to fall somewhere between the two.

The analyses in this paper incorporate the potential impact of generative AI on today’s work activities. The new capabilities of generative AI, combined with previous technologies and integrated into corporate operations around the world, could accelerate the potential for technical automation of individual activities and the adoption of technologies that augment the capabilities of the workforce. They could also have an impact on knowledge workers whose activities were not expected to shift as a result of these technologies until later in the future (see sidebar “About the research”).

Automation potential has accelerated, but adoption to lag

Based on developments in generative AI, technology performance is now expected to match median human performance and reach top-quartile human performance earlier than previously estimated across a wide range of capabilities (Exhibit 6). For example, MGI previously identified 2027 as the earliest year when median human performance for natural-language understanding might be achieved in technology, but in this new analysis, the corresponding point is 2023.

As a result of these reassessments of technology capabilities due to generative AI, the total percentage of hours that could theoretically be automated by integrating technologies that exist today has increased from about 50 percent to 60–70 percent. The technical potential curve is quite steep because of the acceleration in generative AI’s natural-language capabilities.

Interestingly, the range of times between the early and late scenarios has compressed compared with the expert assessments in 2017, reflecting a greater confidence that higher levels of technological capabilities will arrive by certain time periods (Exhibit 7).

Our analysis of adoption scenarios accounts for the time required to integrate technological capabilities into solutions that can automate individual work activities; the cost of these technologies compared with that of human labor in different occupations and countries around the world; and the time it has taken for technologies to diffuse across the economy. With the acceleration in technical automation potential that generative AI enables, our scenarios for automation adoption have correspondingly accelerated. These scenarios encompass a wide range of outcomes, given that the pace at which solutions will be developed and adopted will vary based on decisions that will be made on investments, deployment, and regulation, among other factors. But they give an indication of the degree to which the activities that workers do each day may shift (Exhibit 8).

As an example of how this might play out in a specific occupation, consider postsecondary English language and literature teachers, whose detailed work activities include preparing tests and evaluating student work. With generative AI’s enhanced natural-language capabilities, more of these activities could be done by machines, perhaps initially to create a first draft that is edited by teachers but perhaps eventually with far less human editing required. This could free up time for these teachers to spend more time on other work activities, such as guiding class discussions or tutoring students who need extra assistance.

Our previously modeled adoption scenarios suggested that 50 percent of time spent on 2016 work activities would be automated sometime between 2035 and 2070, with a midpoint scenario around 2053. Our updated adoption scenarios, which account for developments in generative AI, models the time spent on 2023 work activities reaching 50 percent automation between 2030 and 2060, with a midpoint of 2045—an acceleration of roughly a decade compared with the previous estimate. 6 The comparison is not exact because the composition of work activities between 2016 and 2023 has changed; for example, some automation has occurred during that time period.

Adoption is also likely to be faster in developed countries, where wages are higher and thus the economic feasibility of adopting automation occurs earlier. Even if the potential for technology to automate a particular work activity is high, the costs required to do so have to be compared with the cost of human wages. In countries such as China, India, and Mexico, where wage rates are lower, automation adoption is modeled to arrive more slowly than in higher-wage countries (Exhibit 9).

Generative AI’s potential impact on knowledge work

Previous generations of automation technology were particularly effective at automating data management tasks related to collecting and processing data. Generative AI’s natural-language capabilities increase the automation potential of these types of activities somewhat. But its impact on more physical work activities shifted much less, which isn’t surprising because its capabilities are fundamentally engineered to do cognitive tasks.

As a result, generative AI is likely to have the biggest impact on knowledge work, particularly activities involving decision making and collaboration, which previously had the lowest potential for automation (Exhibit 10). Our estimate of the technical potential to automate the application of expertise jumped 34 percentage points, while the potential to automate management and develop talent increased from 16 percent in 2017 to 49 percent in 2023.

Generative AI’s ability to understand and use natural language for a variety of activities and tasks largely explains why automation potential has risen so steeply. Some 40 percent of the activities that workers perform in the economy require at least a median level of human understanding of natural language.

As a result, many of the work activities that involve communication, supervision, documentation, and interacting with people in general have the potential to be automated by generative AI, accelerating the transformation of work in occupations such as education and technology, for which automation potential was previously expected to emerge later (Exhibit 11).

Labor economists have often noted that the deployment of automation technologies tends to have the most impact on workers with the lowest skill levels, as measured by educational attainment, or what is called skill biased. We find that generative AI has the opposite pattern—it is likely to have the most incremental impact through automating some of the activities of more-educated workers (Exhibit 12).

Another way to interpret this result is that generative AI will challenge the attainment of multiyear degree credentials as an indicator of skills, and others have advocated for taking a more skills-based approach to workforce development in order to create more equitable, efficient workforce training and matching systems. 7 A more skills-based approach to workforce development predates the emergence of generative AI. Generative AI could still be described as skill-biased technological change, but with a different, perhaps more granular, description of skills that are more likely to be replaced than complemented by the activities that machines can do.

Previous generations of automation technology often had the most impact on occupations with wages falling in the middle of the income distribution. For lower-wage occupations, making a case for work automation is more difficult because the potential benefits of automation compete against a lower cost of human labor. Additionally, some of the tasks performed in lower-wage occupations are technically difficult to automate—for example, manipulating fabric or picking delicate fruits. Some labor economists have observed a “hollowing out of the middle,” and our previous models have suggested that work automation would likely have the biggest midterm impact on lower-middle-income quintiles.

However, generative AI’s impact is likely to most transform the work of higher-wage knowledge workers because of advances in the technical automation potential of their activities, which were previously considered to be relatively immune from automation (Exhibit 13).

Generative AI could propel higher productivity growth

Global economic growth was slower from 2012 to 2022 than in the two preceding decades. 8 Global economic prospects , World Bank, January 2023. Although the COVID-19 pandemic was a significant factor, long-term structural challenges—including declining birth rates and aging populations—are ongoing obstacles to growth.

Declining employment is among those obstacles. Compound annual growth in the total number of workers worldwide slowed from 2.5 percent in 1972–82 to just 0.8 percent in 2012–22, largely because of aging. In many large countries, the size of the workforce is already declining. 9 Yaron Shamir, “Three factors contributing to fewer people in the workforce,” Forbes , April 7, 2022. Productivity, which measures output relative to input, or the value of goods and services produced divided by the amount of labor, capital, and other resources required to produce them, was the main engine of economic growth in the three decades from 1992 to 2022 (Exhibit 14). However, since then, productivity growth has slowed in tandem with slowing employment growth, confounding economists and policy makers. 10 “The U.S. productivity slowdown: an economy-wide and industry-level analysis,” Monthly Labor Review, US Bureau of Labor Statistics, April 2021; Kweilin Ellingrud, “ Turning around the productivity slowdown ,” McKinsey Global Institute, September 13, 2022.

The deployment of generative AI and other technologies could help accelerate productivity growth, partially compensating for declining employment growth and enabling overall economic growth. Based on our estimates, the automation of individual work activities enabled by these technologies could provide the global economy with an annual productivity boost of 0.5 to 3.4 percent from 2023 to 2040, depending on the rate of automation adoption—with generative AI contributing 0.1 to 0.6 percentage points of that growth—but only if individuals affected by the technology were to shift to other work activities that at least match their 2022 productivity levels (Exhibit 15). In some cases, workers will stay in the same occupations, but their mix of activities will shift; in others, workers will need to shift occupations.

Considerations for business and society

History has shown that new technologies have the potential to reshape societies. Artificial intelligence has already changed the way we live and work—for example, it can help our phones (mostly) understand what we say, or draft emails. Mostly, however, AI has remained behind the scenes, optimizing business processes or making recommendations about the next product to buy. The rapid development of generative AI is likely to significantly augment the impact of AI overall, generating trillions of dollars of additional value each year and transforming the nature of work.

But the technology could also deliver new and significant challenges. Stakeholders must act—and quickly, given the pace at which generative AI could be adopted—to prepare to address both the opportunities and the risks. Risks have already surfaced, including concerns about the content that generative AI systems produce: Will they infringe upon intellectual property due to “plagiarism” in the training data used to create foundation models? Will the answers that LLMs produce when questioned be accurate, and can they be explained? Will the content generative AI creates be fair or biased in ways that users do not want by, say, producing content that reflects harmful stereotypes?

Using generative AI responsibly

Generative AI poses a variety of risks. Stakeholders will want to address these risks from the start.

Fairness: Models may generate algorithmic bias due to imperfect training data or decisions made by the engineers developing the models.

Intellectual property (IP): Training data and model outputs can generate significant IP risks, including infringing on copyrighted, trademarked, patented, or otherwise legally protected materials. Even when using a provider’s generative AI tool, organizations will need to understand what data went into training and how it’s used in tool outputs.

Privacy: Privacy concerns could arise if users input information that later ends up in model outputs in a form that makes individuals identifiable. Generative AI could also be used to create and disseminate malicious content such as disinformation, deepfakes, and hate speech.

Security: Generative AI may be used by bad actors to accelerate the sophistication and speed of cyberattacks. It also can be manipulated to provide malicious outputs. For example, through a technique called prompt injection, a third party gives a model new instructions that trick the model into delivering an output unintended by the model producer and end user.

Explainability: Generative AI relies on neural networks with billions of parameters, challenging our ability to explain how any given answer is produced.

Reliability: Models can produce different answers to the same prompts, impeding the user’s ability to assess the accuracy and reliability of outputs.

Organizational impact: Generative AI may significantly affect the workforce, and the impact on specific groups and local communities could be disproportionately negative.

Social and environmental impact: The development and training of foundation models may lead to detrimental social and environmental consequences, including an increase in carbon emissions (for example, training one large language model can emit about 315 tons of carbon dioxide). 1 Ananya Ganesh, Andrew McCallum, and Emma Strubell, “Energy and policy considerations for deep learning in NLP,” Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics , June 5, 2019.

There are economic challenges too: the scale and the scope of the workforce transitions described in this report are considerable. In the midpoint adoption scenario, about a quarter to a third of work activities could change in the coming decade. The task before us is to manage the potential positives and negatives of the technology simultaneously (see sidebar “Using generative AI responsibly”). Here are some of the critical questions we will need to address while balancing our enthusiasm for the potential benefits of the technology with the new challenges it can introduce.

Companies and business leaders

How can companies move quickly to capture the potential value at stake highlighted in this report, while managing the risks that generative AI presents?

How will the mix of occupations and skills needed across a company’s workforce be transformed by generative AI and other artificial intelligence over the coming years? How will a company enable these transitions in its hiring plans, retraining programs, and other aspects of human resources?

Do companies have a role to play in ensuring the technology is not deployed in “negative use cases” that could harm society?

How can businesses transparently share their experiences with scaling the use of generative AI within and across industries—and also with governments and society?

Policy makers

What will the future of work look like at the level of an economy in terms of occupations and skills? What does this mean for workforce planning?

How can workers be supported as their activities shift over time? What retraining programs can be put in place? What incentives are needed to support private companies as they invest in human capital? Are there earn-while-you-learn programs such as apprenticeships that could enable people to retrain while continuing to support themselves and their families?

What steps can policy makers take to prevent generative AI from being used in ways that harm society or vulnerable populations?

Can new policies be developed and existing policies amended to ensure human-centric AI development and deployment that includes human oversight and diverse perspectives and accounts for societal values?

Individuals as workers, consumers, and citizens

How concerned should individuals be about the advent of generative AI? While companies can assess how the technology will affect their bottom lines, where can citizens turn for accurate, unbiased information about how it will affect their lives and livelihoods?

How can individuals as workers and consumers balance the conveniences generative AI delivers with its impact in their workplaces?

Can citizens have a voice in the decisions that will shape the deployment and integration of generative AI into the fabric of their lives?

Technological innovation can inspire equal parts awe and concern. When that innovation seems to materialize fully formed and becomes widespread seemingly overnight, both responses can be amplified. The arrival of generative AI in the fall of 2022 was the most recent example of this phenomenon, due to its unexpectedly rapid adoption as well as the ensuing scramble among companies and consumers to deploy, integrate, and play with it.

All of us are at the beginning of a journey to understand this technology’s power, reach, and capabilities. If the past eight months are any guide, the next several years will take us on a roller-coaster ride featuring fast-paced innovation and technological breakthroughs that force us to recalibrate our understanding of AI’s impact on our work and our lives. It is important to properly understand this phenomenon and anticipate its impact. Given the speed of generative AI’s deployment so far, the need to accelerate digital transformation and reskill labor forces is great.

These tools have the potential to create enormous value for the global economy at a time when it is pondering the huge costs of adapting and mitigating climate change. At the same time, they also have the potential to be more destabilizing than previous generations of artificial intelligence. They are capable of that most human of abilities, language, which is a fundamental requirement of most work activities linked to expertise and knowledge as well as a skill that can be used to hurt feelings, create misunderstandings, obscure truth, and incite violence and even wars.

We hope this research has contributed to a better understanding of generative AI’s capacity to add value to company operations and fuel economic growth and prosperity as well as its potential to dramatically transform how we work and our purpose in society. Companies, policy makers, consumers, and citizens can work together to ensure that generative AI delivers on its promise to create significant value while limiting its potential to upset lives and livelihoods. The time to act is now. 11 The research, analysis, and writing in this report was entirely done by humans.

Michael Chui is a partner in McKinsey’s Bay Area office, where Roger Roberts is a partner and Lareina Yee is a senior partner; Eric Hazan is a senior partner in McKinsey’s Paris office; Alex Singla is a senior partner in the Chicago office; Kate Smaje and Alex Sukharevsky are senior partners in the London office; and Rodney Zemmel is a senior partner in the New York office.

The authors wish to thank Pedro Abreu, Rohit Agarwal, Steven Aronowitz, Arun Arora, Charles Atkins, Elia Berteletti, Onno Boer, Albert Bollard, Xavier Bosquet, Benjamin Braverman, Charles Carcenac, Sebastien Chaigne, Peter Crispeels, Santiago Comella-Dorda, Eleonore Depardon, Kweilin Ellingrud, Thierry Ethevenin, Dmitry Gafarov, Neel Gandhi, Eric Goldberg, Liz Grennan, Shivani Gupta, Vinay Gupta, Dan Hababou, Bryan Hancock, Lisa Harkness, Leila Harouchi, Jake Hart, Heiko Heimes, Jeff Jacobs, Begum Karaci Deniz, Tarun Khurana, Malgorzata Kmicinska, Jan-Christoph Köstring, Andreas Kremer, Kathryn Kuhn, Jessica Lamb, Maxim Lampe, John Larson, Swan Leroi, Damian Lewandowski, Richard Li, Sonja Lindberg, Kerin Lo, Guillaume Lurenbaum, Matej Macak, Dana Maor, Julien Mauhourat, Marco Piccitto, Carolyn Pierce, Olivier Plantefeve, Alexandre Pons, Kathryn Rathje, Emily Reasor, Werner Rehm, Steve Reis, Kelsey Robinson, Martin Rosendahl, Christoph Sandler, Saurab Sanghvi, Boudhayan Sen, Joanna Si, Alok Singh, Gurneet Singh Dandona, François Soubien, Eli Stein, Stephanie Strom, Michele Tam, Robert Tas, Maribel Tejada, Wilbur Wang, Georg Winkler, Jane Wong, and Romain Zilahi for their contributions to this report.

For the full list of acknowledgments, see the downloadable PDF .

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News & features, winter center, news / weather forecasts, first heat wave of year on horizon for northeast.

While A/Cs will continue to be idle in the Northeast for much of this week, hotter days are just ahead with the first heat wave of the season for millions coming soon.

By Alex Sosnowski , AccuWeather senior meteorologist

Published Jun 10, 2024 9:15 AM PDT | Updated Jun 12, 2024 5:06 AM PDT

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The pattern for the northeastern United States will be a 'tale of two weeks' as low humidity and cool to seasonable air much of this week are replaced with surging heat this weekend and the first heat wave of the season for millions next week, AccuWeather meteorologists say. Opportunities for rain will be limited, a switch from much of the spring.

The upcoming weather will provide some great conditions for summertime activity beginning late this week and continuing through much of next week. For some individuals without air conditioning, though, the upcoming building heat may become a problem.

Cool nights with daytime warming trend into midweek

A dip in the jet stream and high pressure that originated in Canada will continue to keep temperatures and humidity levels under control for much of this week. The same high-pressure zone will tend to keep blossoming tropical moisture in the Gulf of Mexico and the Florida Peninsula at bay.

In the Northeast, temperatures will tend to run within several degrees of the historical average through midweek. Highs during the few days before mid-June will range from near 70 F in northern Maine to the mid-80s in eastern Virginia and the Delmarva Peninsula. Because of the dry air, quick cooldowns will continue in the evenings, with very cool conditions during the overnight hours.

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"Low humidity and mainly clear skies will result in another chilly night for mid-June on Tuesday," AccuWeather Meteorologist Brandon Buckingham said, "From central and western Pennsylvania through upstate New York and a majority of interior New England, temperatures will fall into the 40s and 50s early this week. Farther west across the northern Great Lakes and Upper Midwest, patchy frost will be possible as some locations will dip into the 30s."

However, the region's natural air conditioning that is providing a break in cooling costs will not last much longer.

Late-week temperature spike to tease upcoming heat wave

"As a front approaches from the Great Lakes later this week, a southwesterly breeze will help push temperatures upward on Thursday, with a spike of very warm to hot air in store along much of the Atlantic coast on Friday," Buckingham said.

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By Thursday, widespread highs in the 80s are in store, and by Friday, temperatures along much of the Interstate 95 corridor from the mid-Atlantic to southern New England will spike into the 90s.

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The approaching front may have trouble producing a great deal of rain, but this does not mean there cannot be gusty thunderstorms, including some with damaging wind gusts from Thursday evening across the interior to Friday along part of the I-95 zone .

During Father's Day weekend, temperatures and humidity levels will be in a tug-of-war. Some dry and slightly cooler air will cover the northern parts of the region while heat will hold across the southern zones. The heat will win the battle by early next week.

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Heat wave coming next week

"From Monday through much of next week, home-grown high pressure will build over the region while the jet stream bulges northward," Buckingham explained, "This one-two combination will set the stage for building heat and an uptick in humidity levels. For many, this will be the first heat wave of the year."

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A heat wave is a stretch of unusually hot weather, with or without high humidity, lasting more than two days. For much of the Northeast, the 90-degree mark represents the threshold of warm to hot conditions.

The last heat wave in Philadelphia , where highs were in the 90s for three days or more was Sept. 3-9. Washington, D.C .'s and New York City 's last stretch of 90-degree weather around the same time. In the nation's capital , 90-degree highs occurred consecutively from Sept. 3-8. In New York City , it was Sept. 5-8. Boston struggled to bunch 90-degree days together last summer and hit 90 on only a handful of days.

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From Monday to Thursday of next week, widespread highs ranging from the mid-80s to the mid-90s are in store, with a few spots potentially climbing into the upper 90s. At this level, when combined with intense mid-June sunshine, AccuWeather RealFeel® Temperatures will surge to dangerous levels, especially in the urban areas of many of the major cities.

Because of light winds over the region, coastal areas, including the major cities of Boston and New York City , may be subject to some cooling sea breezes on certain days, where temperatures are held 10-20 degrees lower than areas several miles inland.

"Aside from the possibility of a shower or gusty thunderstorm from the front late this week, areas that miss out on the rain could have a stretch of where it does not rain at all for seven to 10 days or more," AccuWeather Senior Meteorologist Dave Dombek said, "The dryness will help temperatures surge during the day as much of the sun's energy won't be used up evaporating moisture from the ground."

Rainfall in much of the Northeast since March 1 was 100-150% of the historical average. However, parts of the Northeast were very wet during March, with 150-300% rainfall compared to the historical average.

The dry weather for most days well past mid-June will provide opportunities for outdoor projects to be undertaken, run on schedule or completed.

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  1. 10. Traveling Waves

    MIT 8.03SC Physics III: Vibrations and Waves, Fall 2016View the complete course: https://ocw.mit.edu/8-03SCF16Instructor: Yen-Jie LeeProf. Lee introduces the...

  2. 16.2: Traveling Waves

    The magnitude of the wave velocity is the distance the wave travels in a given time, which is one wavelength in the time of one period, and the wave speed is the magnitude of wave velocity. In equation form, this is. v = λ T = λf. (16.2.1) (16.2.1) v = λ T = λ f.

  3. PDF any

    principal advantage of the exponential form is based on the fact that the product of two exponentials is the exponential of the sum of their arguments. This is also the basis of multiplying by adding logarithms on a slide rule. We write a traveling wave such as f = A cos(k z - omega t) in exponential

  4. Traveling waves

    Traveling waves. A wave pulse is a disturbance that moves through a medium. A periodic wave is a periodic disturbance that moves through a medium. The medium itself goes nowhere. The individual atoms and molecules in the medium oscillate about their equilibrium position, but their average position does not change. As they interact with their ...

  5. 16.3: Mathematics of Waves

    Pulses. A pulse can be described as wave consisting of a single disturbance that moves through the medium with a constant amplitude. The pulse moves as a pattern that maintains its shape as it propagates with a constant wave speed. Because the wave speed is constant, the distance the pulse moves in a time Δt is equal to Δx = vΔt (Figure \(\PageIndex{1}\)).

  6. PDF Wave conventions: the good, the bad and the ugly

    while a wave travelling from right to left is described by y = exp[i( kx !t)]: (2) Note that a positive term before the x means a wave travelling towards positive x. This convention is used in quantum mechanics where a wave of the form (1) corresponds to a particle moving with velocity ~k=m. 1.2 The electromagnetism convention

  7. PDF 4. OSCILLATIONS AND WAVES

    This is the equation of motion of a travelling wave, or the wave equation! Wave Equation: d2y(x,t) dx2 − 1 v2 d2y(x,t) dt2 = 0 The wave equation is a second order differential equation in space and time. In order to solve this equation we assume that the following wave function might be a solution of the wave equation: y(x,t) = A·sin(kx− ...

  8. 8: Traveling Waves

    A traveling wave in a linear system is a pair of standing waves put together with a special phase relation. We show how traveling waves can be produced in finite systems by appropriate forced oscillations. We then go on to discuss the force and power required to produce a traveling wave on a string, and introduce the useful idea of "impedance

  9. Understanding the mathematical representation of a travelling plane wave

    The exponential term I am assuming to be the phase term which tells us how the phase of the wave evolves with time. My issue is that when writing out the x component of the above, I would've thought $\Psi_x = A_xe^{i(k_x r_x -wt)}$ , whereas in reality, $\Psi_x = A_xe^{i(\vec{k} \cdot \vec{r}-wt)}$ .

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  11. Complex representation for traveling waves

    The effect of propagating a wave a distance (measured as a positive value whether the wave moves to the right or left) appears in the complex representation as multiplication by the complex phase factor . For plane waves and waves moving in one dimension, this is the only factor. If the wave spreads out from a point in two or three dimensions ...

  12. Periodic travelling wave

    In mathematics, a periodic travelling wave (or wavetrain) is a periodic function of one-dimensional space that moves with constant speed. Consequently, it is a special type of spatiotemporal oscillation that is a periodic function of both space and time.. Periodic travelling waves play a fundamental role in many mathematical equations, including self-oscillatory systems, excitable systems and ...

  13. PDF 2. Waves and the Wave Equation

    Later, we will derive the wave equation from Maxwell's equations. Here it is, in its one-dimensional form for scalar (i.e., non-vector) functions, f. 2. f. x. 2 1 v 2 2 f t 2 0. This equation determines the properties of most wave phenomena, not only light waves. water wave. air wave earth wave.

  14. Travelling waves

    Q: What are the units of the wave number? The answer . Using the wave number, one can write the equation of a stationary wave in a slightly more simple manner: In order to write the equation of a travelling wave, we simply break the boundary between the functions of time and space, mixing them together like chocolate and peanut butter.

  15. Plane wave

    Plane wave. In physics, a plane wave is a special case of wave or field: a physical quantity whose value, at any moment, is constant through any plane that is perpendicular to a fixed direction in space. [1] For any position in space and any time , the value of such a field can be written as. where is a unit-length vector, and is a function ...

  16. Travelling Waves

    Describing a Wave. A wave can be described as a disturbance in a medium that travels transferring momentum and energy without any net motion of the medium. A wave in which the positions of maximum and minimum amplitude travel through the medium is known as a travelling wave. To better understand a wave, let us think of the disturbance caused ...

  17. Why can we model a travelling wave with an exponential?

    Hi, I'm currently studying solid-state physics and learning about phonons. We solved a simple model in class using an assumed travelling wave solution were the displacement as a function of time was

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    0:00. 0:24. The Centers for Disease Control and Prevention data shows that a new COVID variant, the KP.3 variant, is rising to dominance across the United States. For the two-week period starting ...

  19. 2.3: Representation of Waves via Complex Functions

    A one-dimensional wavefunction takes the general form. ψ(x, t) = Acos(kx − ωt + φ), where A is the wave amplitude, k the wavenumber, ω the angular frequency, and φ the phase angle. Consider the complex wavefunction. ψ(x, t) = ψ0ei ( kx − ωt), where ψ0 is a complex constant. We can write ψ0 = Aeiφ, where A is the modulus, and φ ...

  20. The Oracle of Omaha Meets AI: Is Berkshire Hathaway Prepared for

    This analysis is rapidly becoming an urgent necessity, as AI is poised to enter a period of unprecedented, exponential growth. The convergence of advancements in computing power and the massive ...

  21. National Travel Attitudes Study: Wave 10

    Details. In NTAS wave 10: among people aged 65 years and over, 81% own, or are in the process of acquiring, a concessionary bus pass. of users who were aware of the bus fare cap, 49% say they have ...

  22. How to get "complex exponential" form of wave equation out of

    But we wouldn't normally proceed by replacing sin by this expression. Both the sin form and the exponential form are mathematically valid solutions to the wave equation, so the only question is their physical validity. In QM we don't worry about having a complex solution because the observable is the squared modulus, which is always real.

  23. Greece shuts Acropolis to protect tourists from blistering heat

    A visitor holds an umbrella on top of the Acropolis hill during a heatwave, in Athens, Greece in June 11, 2024. In July, the site was also closed between 12 p.m and 5 p.m. in an effort to protect ...

  24. Here It Comes: Another Hot Summer in Europe

    By Ceylan Yeğinsu. May 24, 2024. Europe, the world's fastest-warming continent, is headed for another scorching summer, meteorologists warn. And travelers, once again, are heading to the hot ...

  25. Opinion

    Mr. Lemley is a professor at Stanford Law School. Mr. Wansley is an associate professor at Cardozo School of Law. Silicon Valley prides itself on disruption: Start-ups develop new technologies ...

  26. Hajj 2024: Saudi Arabia braces for extreme heat

    As Saudi Arabia prepares for Hajj 2024, rising temperatures pose significant challenges. Officials warn of extreme heat, prompting enhanced cooling measures for pilgrims.

  27. quantum mechanics

    For example, if you have a potential that goes to infinity at some point (e.g. infinite square well), you know that the wavefunction becomes zero there, and thus it's to your advantage to choose a basis where the basis functions actually do go to zero somewhere: the sine/cosine basis, rather than the exponential one.

  28. Economic potential of generative AI

    The speed at which generative AI technology is developing isn't making this task any easier. ChatGPT was released in November 2022. Four months later, OpenAI released a new large language model, or LLM, called GPT-4 with markedly improved capabilities. 1 "Introducing ChatGPT," OpenAI, November 30, 2022; "GPT-4 is OpenAI's most advanced system, producing safer and more useful ...

  29. is this function a traveling wave?

    One by one. You ask wether f(x) = sin(x2 −t2) f ( x) = sin. ⁡. ( x 2 − t 2) is a travelling wave. The answer is "no, it isn't", with the usual definition of wave. The reason is that that function does not satisfy the wave equation. It's as easy as that: it doesn't satisfy the wave equation → it is not a wave.

  30. First heat wave of year on horizon for Northeast

    A heat wave is a stretch of unusually hot weather, with or without high humidity, lasting more than two days. For much of the Northeast, the 90-degree mark represents the threshold of warm to hot ...