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

(F.1)

where *m** is the mass per unit length, which is roughly ^{1}⁄_{2}*ρh*(*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

(F.2)

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:

(F.3)

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