with the group velocity appropriate to waves with a period T/n, 
and the edges are modulated by the Fresnel pattern discussed in 
detail in Chapter 5. The first train has a period of t seconds 
and an amplitude of (WTA/¢ Tt) exp(-(27/ - on/t)°/4o0°. The 
second train has a period of 1/2 seconds and an amplitude of 
(Wri/fg tT) exp(-(272/r - or/t)°/4a 7). The periods of the waves 
which would propagate into the area of decay, for tT = 100 seconds, 
would be 100 seconds, 50 seconds, 33.3 seconds, 25 seconds, 20 
seconds, 16.7 seconds, 14.3 seconds, 12.5 seconds, 11.1 seconds, 
10 seconds, and so forth through 4 seconds for m = 25, 2 seconds 
for m = 50, and 1 second for m= 100. If T were 10 seconds the 
train with a 10 second period would have a maximum amplitude and 
for typical values of o the trains with one and one hundred second 
periods would be very low. 
For the values of o = 1/20 sec +, T = 10 sec, and A = 5 meters, 
and for tT = 100 seconds, the amplitude of the 100 second component 
would be less than 10722 
meters, and the amplitude of the 10 second 
component would be 3.55 meters. 
If p were equal to 180, the wave system represented by equa- 
tion (6.4) would require ten hours and two minutes (36,100 seconds) 
to pass the point x = 0. From the derivation, this wave system 
can be broken down into a number of wave trains of different 
spectral periods and each wave train would advance with its own 
group velocity into the area of decay. Each wave train would take 
essentially 10 hours to pass a point in the area of decay, but 
they would pass at different times. 
For the chosen values of parameters for equation (6.4), only 
m= 
