The graph between wave number (\bar{v}) and angular frequency (... | Filo
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Two waves have the same angular frequency ω, wave number k and amplitude A, but they differ in phase: y1=A cos(k x-ωt) and y2=A cos(k x-ωt ϕ) . Show that their superposition is also a simple harmonic wave, and determine its amplitude as a function of the phase difference ϕ | Numerade
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SOLVED: The angular frequency of the surface waves in a liquid in terms of the wave number k is given by ω, where Ï is the density of the liquid, and σ is the surface tension. The relation between phase velocity Vp and group velocity Vg of the surface waves is:Vg = Vp / (1 - Vp/Vg)
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Show that for those waves whose angular frequency ωand wave number k obey the dispersion relation k^2 c^2=ω^2 constant, the product of the phase and group velocities is equal to c^2 ^v gp h=c^2, where c is the speed of light. | Numerade
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