must _be exactly two seconds. 
Suppose that the period is not exactly two seconds at the sec- 
ond point of observation. Suppose, for example, that the period is 
really 2.01 seconds. Near the generator the period is two seconds. 
Each periodic motion at the first point of observation means that 
one wave crest has progressed toward the second point of observa- 
tion. In the next one hundred hours, then, 180,000 waves will pass 
the first point of observation. At the second point of observation, 
where the period is assumed (erroneously) to be 2.01 seconds only 
179,104 waves will pass during the time of observation. Thus 896 
But at the start, it was assumed that the motion had settled down 
to a steady state; and now it is found that the number of wave crests 
between the two points is continuously increasing. The assumption 
that the period is not the same is therefore wrong. Therefore the 
period at the second point of observation must be exactly the same 
as at the first point of observation. 
It might be remarked that a formal exact mathematical solution 
to the experiment just described has never been obtained. The works 
of Stoker [1947] and Eckart [1951] come close to solving the problem, 
but Stoker's solution for a linear sloping beach although exact, as 
far as the linear theory goes, is not quite a solution to this 
problem and Eckart's methods would yield only an approximation to 
the true solution. 
Finally, though, the important point is that whatever solution 
is found the period of the motion at the second point must be the 
same as at the first point. Also the wave speed at the second point 
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