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SOLVED: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.
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The angular frequency of the surface waves in a liquid is given in terms of the wave number k by ω = √(gk (T/ρ)), where g is the acceleration due to gravity, ρ is the density of the liquid, and T is the surface tension (which gives an upward force on an element of the surface liquid). Find the phase and group velocities for the limiting cases when the surface waves have: (a) very large wavelengths and (b) very small wavelengths.
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