The phase velocity v of gravity waves in a liquid of depth h is given by the formula v = 8 tanh kh, k where g is the acceleration of free fall and k = 2w/2 is the wavenumber, a being the wavelength. Sketch the dispersion relation for such waves, and show that the group velocity is always between v2 and v. Find the phase and group velocities for gravity waves of frequency 1 Hz in a liquid of depth 0.1 m.

The phase velocity v of gravity waves in a liquid of depth h is given by the formula v = 8 tanh kh, k where g is the acceleration of free fall and k = 2w/2 is the wavenumber, a being the wavelength. Sketch the dispersion relation for such waves, and show that the group velocity is always between v2 and v. Find the phase and group velocities for gravity waves of frequency 1 Hz in a liquid of depth 0.1 m.