Question

The dispersion relation for capillary-gravity waves on the surface of water ω = (gk + σk^3/ρ)^1/2. Here g = 9.81 m/s is the acceleration due to gravity,σ = 0.047 N/m is the surface tension of water, and = 1000kg/m3 is its density. Calculate the group velocity for these waves and plot it as a function of wavelength λ, where of course λ = 2π/k. The group velocity is a minimum for a particular value of λ. What is that value, and what is the group velocity there? For smaller wavelengths, the wave motion is governed mostly by surface tension, while for longer wavelengths gravity is dominant.

Answer 1

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