function of x and t alone at that end of the tank. Twenty miles 
away let the depth shoal gradually and linearly over a distance of 
ten miles to a final depth of five feet. For another twenty miles 
let the depth remain at five feet and then let the tank be ended by 
a perfect wave absorber without any reflection. Suppose also that 
the generator has been running for about two months so that all 
transient effects can be ignored. Finally let the amplitude of the 
waves at the generator be two inches so that the small height assump- 
tion can be used as an approximation. 
Now, at a distance of five miles from the generator, the waves 
will have a speed given by c? = gor /4r@ = gL/2r. Exactly one sinu- 
soidal crest will pass the point of observation every two seconds. 
The wave record will be essentially a pure sine wave if observed at 
a fixed point. The period of the wave will be exactly two seconds. 
At a distance of forty five miles from the generator, the waves 
will have passed over the sloping bottom, and at a distance of fifteen 
miles from the slope, since the deep water wave length is only one 
two hundredth and sixty fourth of a mile, the waves in the region 
ought to be again nearly sinusoidal in form and the crests ought to 
be traveling again with a constant speed. The crest speed ought to 
be given by equation (12.1) from classical theory. 
A long time ago in Chapter 2, under the assumption that the 
motion was purely periodic with one discrete spectral period, a 
periodicity factor in time for depth still variable was split off 
from the potential equation. The above experiment has been designed 
to show why this assumption is valid. Suppose that at this second 
point of observation the period of the wave is recorded. The period 
26 
