Chapter 5. THE PROPAGATION OF A FINITE WAVE TRAIN 
IN INFINITELY DEEP WATER 
Introduction 
There is considerable interest in the problem of what hap- 
pens to a train of waves of constant height, finite duration, 
and constant apparent local period as it travels along. Sver- 
drup and Munk [1947] have given a physical argument based upon 
the fact that the energy of the wave train advances with the 
group velocity which shows that the major rise of the amplitude 
advances with the group velocity of the apparent local period 
and that only very low waves travel out in front of the main 
group. 
Such a finite wave train has a continuous Fourier spectrum. 
In order to determine the effects of dispersion, it is necessary 
to investigate the problem mathematically with the techniques 
of the previous problem. 
Despite Munk's [1947] assertion to the contrary, dealing 
with the recorded period, "without recourse to the nature of 
the underlying continuous Fourier spectrum" always tacitly assumes 
something about the underlying spectrum which may not be theo- 
Tetically justified. There is considerable confusion in the 
technical literature about the difference between the apparent 
local period of the previous section and the period of a periodic 
function. In addition the use of the formula c = gT/2r in the 
above reference is not valid because the formula applies only 
to a purely periodic wave train of one constant period. 
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