--- title: "Meaning & Key Takeaway of: The function ei(kx-ωt) represents a wave…" description: "\"“The function ei(kx-ωt) represents a wave that travels at a speed of ω/k, which we have just shown to be equal to -k2. Therefore, the different plane-w..." image: "https://sms4smile.com/quotes/i/49c/timothy-gowers-30245_theory_the-function-ei-kx-t-represents-a-wave-t_384096.png" --- # The function ei(kx-ωt) represents a wave that travels at a… ![“The function ei(kx-ωt) represents a wave that travels at a speed of ω/k, which we have just shown to be equal to -k2. Therefore, the different plane-wave components of the solution travel at different speeds: the higher the angular frequency, the greater the speed. For this reason, the equation…” quote by Timothy Gowers](https://sms4smile.com/quotes/i/49c/timothy-gowers-30245_theory_the-function-ei-kx-t-represents-a-wave-t_384096.png) [Download](https://sms4smile.com/quotes/i/49c/timothy-gowers-30245_theory_the-function-ei-kx-t-represents-a-wave-t_384096.png) [Open image](https://sms4smile.com/quotes/i/49c/timothy-gowers-30245_theory_the-function-ei-kx-t-represents-a-wave-t_384096.png) > ““The function ei(kx-ωt) represents a wave that travels at a speed of ω/k, which we have just shown to be equal to -k2. Therefore, the different plane-wave components of the solution travel at different speeds: the higher the angular frequency, the greater the speed. For this reason, the equation (1) is called dispersive.”” [Timothy Gowers](https://sms4smile.com/quotes/author/timothy-gowers/) ## About This Quote This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation. Dispersive equations cause different wave components to travel at varying speeds, leading to wave spreading. **In simple terms:** Wave parts move at different speeds, causing spread. Key Takeaway Recognize dispersion when analyzing wave behavior. Themes physics waves mathematics Mood analytical technical Type scientific educational When to use this quote - optics - acoustics - quantum mechanics - engineering simulations Key Concepts dispersion phase velocity Questions to Reflect On - How does dispersion affect signal transmission? - When is dispersion beneficial? A Different Perspective Not all systems are dispersive; some are non‑dispersive. ★ ★ ★ ★ ★ No ratings yet [Travel](https://sms4smile.com/quotes/about/travel/) ## Related quotes > [“the simple algebraic equation ω+k3 = 0. 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