III-62 



Most of t±ie velocity measurements were confined to frequencies less 

 than the resonant frequency for the air bubbles in the mixture, but some were 

 also made at greater frequencies. (See Figures III-27c and III-27g.) The agree- 

 ment between theory and experiment can be considered satisfactory. The results 

 confirm the theoretical predictions that 



1 . as the incident frequency approaches the resonant fre- 

 quency from below, the phase velocity decreases rapidly 



2 . for incident frequencies above resonance, the phase 

 velocity is greater than in the bubble-free water. 



Attenuation measurements did not always compare as satisfactorily 

 with the theory as velocity measurements, but the theory certainly provides a 

 useful estimate. The percentage discrepancy is considerably larger for fre- 

 quencies at or above resonance than for lower frequencies, which might be over- 

 looked because of the logarithmic scale . Some of this may be due to the equip- 

 ment, which was not designed to handle such high attenuations. For frequencies 

 below resonance, the attenuation measurements are generally a little larger 

 than the theory predicts . Some of this was attributed to the noise level in the 

 system. 



C. SCATTERING BY MARINE ORGANISMS 



Scattering in the ocean is due in part to marine objects such as fish, 

 plants and debris. The principal effect of these scatterers is to cause volume 

 reverberation (i.e., back scattering) and attenuation of the propagating sound. 



A convenient method of measuring such scattering is to radiate the 

 sound in a succession of pulses, each of which is short compared with the in- 

 terval between pulses. The transducer receives back- scattered energy be- 

 tween pulses which has come from scatterers farther and farther from the 

 source as time-after-pulse increases. It is expected that, since the pulse of 

 sound forms an expanding spherical shell of constant thickness, it will gener- 

 ally be scattered by many objects in the water and numerous scattered waves 

 will arrive simultaneously at the receiver. The usual treatment is based on 

 this assumption; that is, at any instant, scattering from many individual objects 

 is superposed. It is convenient to define a scattering coefficient, m, of a unit 

 volume, analogous to the back- scattering cross section of an individual scat- 

 terer. 



The phenomenon of volume reverberation has been studied at great 

 length. Considerable data have been amassed, which have been very well sum- 

 marized by Urick and Pryce (Ref. III-41) and will not be presented here in detail. 



Arthur B.ILittlcJnc-. 



S-7 001-03 07 



