Summary of wave group behavior 
In summary, the wave group studied travels forward with 
the group velocity appropriate to the value of T employed. It 
dies down in amplitude as it travels along and spreads out over 
the ocean surface. The individual waves under the envelope 
form in the rear of the envelope es waves with a short apparent 
local period, travel through the envelope with a gradually in- 
creasing apparent local period to a maximum amplitude where 
they have an apparent local period nearly equal to T, and finally 
race ahead with a longer and longer apparent local period to 
disappear at the front of the group. At any instant of time, 
the longest apparent waves are at the front of the group, if 
x and t are greater than zero. 
The study in this section of the behavior of the solution 
for values of the parameters employed in the tables is now com- 
pleted. A study of the pressure caused by the surface disturbance 
will be made in a later chapter. 
New form of Cauchy-Poisson problem 
One very special modification of the solution can be found 
which yields another fascinating form of the Cauchy-Poisson wave 
problem. If in equation (4.1), sin 27t/T is replaced by cos 2rt/Z, 
then in equation (4.9), the negative sine term can be replaced 
by a positive cosine term. Then in these new equations replace 
A by a modified form given in equation (4.34), where A* is constant. 
As o approaches infinity, the modified form of equation 
(4.1) approaches an infinitely hign spike which lasts only for 
an instant in time. The spectrum given by a(y) is equal to 
Sane 
