behind. It now occupies a previously undisturbed area to 

 which it has brought energy E/4. In the meantime, a second 

 wave has been generated, occupying the position next to the 

 plunger where E/4 was left behind by the first wave. The 

 energy of this second wave equals E/4 + E/2 = 3E/4. Repeated 

 applications of this reasoning lead to the results shown in 

 Table 2-1. 



Table 2-1. Distribution of wave heights in a 

 short train of waves. 



"The series number n gives the total number of waves present 

 and equals the time in periods since the first wave entered 

 the area of calm; the wave number m gives the position of the 

 wave measured from the plunger and equals the distance from 

 the plunger expressed in wave lengths. In any series, n, the 

 deviation of the energy from the value E/2 is symmetrical 

 about the center wave. Relative to the center wave all waves 

 nearer the plunger show an excess of energy and all waves 

 beyond the center wave show a deficit. For any two waves at 

 equal distances from the center wave the excess equals the 

 deficiency. In every series, n, the energy first decreases 

 slowly with increasing distance from the plunger, but in the 

 vicinity of the center wave it decreases rapidly. Thus, 

 there develops an "energy front" which advances with the 

 speed of the central part of the wave system, that is, with 

 half the wave velocity. 



"According to the last line in Table 2-1 a definite pattern 

 develops after a few strokes: the wave closest to the plung- 

 er has an energy E(2'^-l)/2'^ which approaches the full 

 amount E, the center wave has an energy E/2, and the wave 

 which has traveled the greatest distance has very little 

 energy (E/2°)." 



With a large number of waves (a large n) , energy decreases with increasing 

 m, and the leading wave eventually loses its identity. At the group center, 

 energy increases and decreases rapidly — to nearly maximum and to nearly zero. 

 Consequently, an energy front is located at the center wave group for deep- 

 water conditions. If waves had been examined for shallow rather than deep 

 water, the energy front would have been found at the leading edge of the 



2-30 



