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 1⁄2ρh(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