For a wave of wavelength λ and period T, if the height of each crest
and depth of each trough is h = 1 m, the potential energy passing per unit
time, per unit length, is


where m* is the mass per unit length, which is roughly 12ρh(λ/2) (approx-
imating the area of the shaded crest in figure F.2 by the area of a triangle),
and h is the change in height of the centre-of-mass of the chunk of elevated
water, which is roughly h. So


To find the potential energy properly, we should have done an integral
here; it would have given the same answer.) Now λ/T is simply the speed
at which the wave travels, v, so:


Waves have kinetic energy as well as potential energy, and, remarkably,
these are exactly equal, although I don’t show that calculation here; so the
total power of the waves is double the power calculated from potential

Figure F.2. A wave has energy in two forms: potential energy associated with raising water out of the light-shaded troughs into the heavy-shaded crests; and kinetic energy of all the water within a few wavelengths of the surface – the speed of the water is indicated by the small arrows. The speed of the wave, travelling from left to right, is indicated by the much bigger arrow at the top.