The phase velocity v of gravity waves in a liquid of depth h is given by the formula v2 g k tanh kh, where g is the acceleration of free fall and k 2 is the wave number, being the wave length Sketch the dispersion relation for such waves, and show that the group velocity is always between v 2 and v...

First we need to deduce the form of the dispersion relation k which we can do by using the fact that ...

The phase velocity v of gravity waves in a liquid of depth h is given by the

Question:

The phase velocity v of gravity waves in a liquid of depth h is given by the formula

v2 = g/k tanh kh,

where g is the acceleration of free fall and k = 2π/λ is the wave number, λ being the wave length. Sketch the dispersion relation for such waves, and show that the group velocity is always between v/2 and v. Find the phase and group velocities for gravity waves of frequency 1 Hz in a liquid of depth 0.1m.