Formulation 
Suppose that a wave record defined by equation (5.1) is ob- 
served at the point x = O and y = 0, as a function of time. The 
sea surface would be perfectly flat for all times before t = -ntT. 
After that time waves all of the same height with an apparent 
local period equal numerically to T would be observed until t = nf. 
There would be 2n complete wave crests. After t = nT the sea sur- 
face would become and remain flat again. Thus the wave train lasts 
only for a finite length of time, and it is therefore referred to 
as a finite wave train. It would be nice to know what the sea sur- 
face looks like at other places and other times. It would also be 
nice to know how the pressure varies as a function of depth as the 
wave train passes overhead. 
Method of solution 
The continuous spectrum, b(y), can be found as usual by in- 
tegrating equation (5.2). The last result in equation (5.2) has 
the same property that was found in the previous chapter in that 
for > O the second term dominates the first term. 
By arguments exactly parallel to the ones in the previous 
chapter, the equation for the free surface can be written in the 
form of equation (5.3). For x = 0, equation (5.3) reduces to equa- 
ealoja\ (Cojpabe 
It was possible to obtain a representation for the pressure 
caused by the disturbance in an integral form similar to equation 
(4.7) of the previous section. However the indicated integration 
could not be carried out, so, although it would be nice to know 
something about the pressure caused by the disturbance, that aspect 
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