That is, ninety percent of the time the spectriijii will be expected to lie 

 between the two dashed ciirves • 



Another set of calc-ulations was made using a relationship between the 

 average wave length L and the average period "T" of a wave system, 

 introduced by Pierson (1952). If it is assumed that 



holds over a narroxir spectral band width, then it can be substituted in the 

 expression 



in which /L =■ ^TtJt 



and 



C05K' [(/tc'cl/^^ \^doVK C/a'i/^il 



is the attenuating factor at depth d • Itcoth {IL d /a ") is the 



iterated hj'perbolic cotangent of /JToiJ^ t ai^d 



This factor K* , when applied to the surface power spectrum mentioned 

 above , determined a pressure power spectrum much smaller than the true spectrum 

 obtained from the analysis of the pressure record. In effect, making this 

 substitution changed the attenuating factor from 



L Hro \ , ^Kere (j, = ^ 



The behavior of these finntions is shoiTO in figure 3- The results reported 



9 



