ECHOES FROM SUBMARINE WAKES 



523 



recorder traces and oscillograms. Reverberation, par- 

 ticularly at long ranges, imposes an upper limit to the 

 practicable pulse length. 



Rather different considerations govern the choice 

 of pulse length for fundamental research into the 

 physical constitution of wakes. The aim of such work 



which the internal density distribution is undergoing 

 all the time, aside from echo fluctuations due to ran- 

 dom interference and variable transmission loss. Only 

 by averaging numerous instantaneous profiles could a 

 truly representative picture of the n{x) distribution 

 be obtained. 



Table 3. Wake indices. 



may be either to establish the overall properties of a 

 wake, or to resolve its microstructure. In the first 

 case the use of long signals, overlapping the entire 

 wake, is indicated, whereas in the second case maxi- 

 mum resolving power is achieved by extremely short 

 pulses. According to equation (40) the wake strength 

 determined with long pulses is a function of (1) the 

 depth of the wake, (2) the average cross section for 

 scattering and extinction by the bubble population, 

 and (3) the acoustic thickness <JeN{w) of the entire 

 wake, which may be determined quite independently 

 by measurement of the horizontal transmission loss. 

 Therefore, a simultaneous observation of the echoes 

 returned by the wake and of the horizontal transmis- 

 sion loss through it offers the greatest promise for 

 testing the adequacy of equation (40) for long signals. 

 The corresponding equation (39) for short pulses has 

 been derived by neglecting the microstructure of the 

 wake, by putting n{x) = constant = n. However, on 

 inspection of the rigorous equation (24), it will be 

 seen that the echo profile on the oscillogram is es- 

 sentially proportional to the function 



nix)e 



-2ajf(x) 



for the case of extremely short signals, and of an ideal 

 sharp sound beam which could be realized approxi- 

 mately by placing the transducer very close to the 

 wake. Such an analysis of the microstructure of 

 wakes by short-pulse echoes would be of rather 

 limited practical value, because of the rapid changes 



As to signals of intermediate length, it may be pre- 

 sumed that equation (39) will represent the •"•ariation 

 of W with To reasonably well. 



33.2.3 



Frequency 



Most echo ranging at wakes has been carried out 

 with frequencies between 20 and 60 kc. The available 

 observations suggest a conspicuous variation of wake 

 strength with frequency, but no such dependence can 

 be anticipated theoretically. The dominant factor 

 tTs/ffj in the formula for the wake strength does not 

 change much with frequency, for bubbles of resonant 

 size. At present little is known about the relative 

 proportion of resonant bubbles in the total popula- 

 tion and how this proportion changes with time; but 

 there is no definite reason to believe that bubbles of 

 nonresonant size predominate, in which case as/ve 

 would vary more markedly with frequency. In any 

 event, the influence of (r,/(r<, on the wake strength 

 would not be expected to account for more than a few 

 decibels. However, some frequency effect may result 

 from the factor (1 - e'^"^^'"^), provided that the 

 wake is highly transparent ; otherwise the exponential 

 would be small compared with 1. 



33.3 ECHOES FROM SUBMARINE WAKES 



Quantitative data on the strength of submarine 

 wakes have recently been computed from the original 

 measurements of echo levels. Some of these have been 



