Under these conditions, waves would leave the forward edge 
of the fetch while the winds are blowing over the fetch throughout 
the duration of the storm. But when the winds stop, there would 
also be a distance, F, behind the point, x = 0, such that for any 
point between x = O and x = = F there would be essentially the 
Same time power spectrum for the waves as at the origin. The 
time power spectrum must be measured over a short enough time 
interval and at a time near t = Dg. 
Consider the effect of operating on 7(0,t) as given by 
equation (7.35) with a new envelope function Fa(t, + ) at the 
source. The effect of F,(t,u) on 1(0,t) is by the definition 
of the integral the same as the limiting effect of Fp(t, #) op- 
erating on a partial sum as the net of the partial sum goes to 
zero; and, as before, it is only necessary to consider the effect 
of Fa(t, #) upon one sine wave in the partial sum. 
At x = 0, no wave component of spectral frequency, p WD? is 
observed for t less than zero. At t = 0, it appears instantaneous- 
ly and at full amplitude to last at least until t equals the dura- 
tion of the storn, Da. The wave component does not cease when 
t = De because it still exists over the fetch. The rear edge of 
the component must travel a distance F to reach the origin, and, 
if the spectral frequency is pu 1 and if the rear edge travels 
with the group velocity, then an additional time given by 
24,F/g is required. After t = D, + 2u4,F/g, this particular 
component will no longer be present. 
F(t) as given by equation (7.51 formulates these conditions 
for w variable. The higher frequency (shorter period) components 
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