Experiments on water waves show that the speed of waves in shallow water is independent of...

Experiments on water waves show that the speed of waves in shallow water is independent of their wavelength (see Problem). Using this observation and dimensional analysis, determine how the speed v of shallow-water waves depends on the depth of the water, d, the mass per volume of water, p, and the acceleration of gravity, g.

Problem

Shallow-Water Waves In shallow water of depth d the speed of waves is approximately . Find the speed and frequency of a wave with wavelength 0.75 cm in water that is 2.6 cm deep.