1. So in deep water the phase speed increases with the wavelength, and with the period. 2. The limiting value of the phase speed for " m " j " 1 directly results. 3. Water waves of different wave lengths travel with different phase speeds , a phenomenon known as frequency dispersion. 4. In deep water the groups travel at a group velocity which is half of the phase speed . 5. For very long waves ( as the zonal wavenumber approaches zero ), the non-dispersive phase speed is approximately: 6. Since this shallow-water phase speed is independent of the wavelength, shallow water waves do not have frequency dispersion. 7. Another property of non-linear waves is that the phase speed of non-linear waves depends on the wave height. 8. This is a nonlinear effect, by which waves of larger amplitude have a different phase speed from small-amplitude waves. 9. Therefore, these waves are non-dispersive ( because the phase speed is not a function of the zonal wavenumber ). 10. First the surface elevation, and thereafter the phase speed , of the cnoidal waves for infinitesimal wave height will be examined.
