
 Surface Waves 
  Then, the time derivative of the velocity potential is equal to the potential of the external forces, here gravitation, when evaluated at the free surface, where the pressure is constant regardless of displacement, and may be taken as zero. 
  The energy in the wave is moving at the speed of the group, not at the phase velocity of the waves. 
  If the phase velocity is plotted as a function of wavelength, a tangent from any point intercepts the velocity axis at the group velocity U, as shown on the left in the figure. 
 www.du.edu /~jcalvert/waves/surfwave.htm (1857 words) 
