SECT. 4] SOUND SCATTERING BY MARINE ORGANISMS 519 



since p changes very slowly with depth. Generally, large migrations in depth 

 amount to considerable change in temperature as well. The ocean temperature 

 almost everywhere decreases with increasing depth. The effect of temperature 

 on 1/i? is approximately (1/T)'^ Usually the temperature change will have the 

 effect of reducing the frequency change by a small amount (order of 2% for a 

 change of 20°C). 



The swim-bladders of bathypelagic fishes are not generally spherical but are 

 more nearly like prolate spheroids (Marshall, 1951). Furthermore they probably 

 do not behave strictly as "free" bubbles but are constrained by the body of 

 the fish. Scattering by a prolate spheroidal bubble can be shown to have a 

 resonant frequency which varies as P'/^ if the bubble size and shape remain 

 constant. If the gas content remains constant and the bubble is free to com- 

 press in all directions, then the resonant frequency varies as P'l^, as for the 

 spherical bubble. However, if the bubble is constrained so that it will not 

 shorten its major diameter, but will compress by becoming "slimmer", then 

 the resonant frequency varies very nearly as P. This latter possibility seems 

 plausible because the structure of the fish leaves it freer to compress in this 

 way.i Unfortunately no experimental studies have been made of single speci- 

 mens over a sufficiently great frequency range to permit the evaluation of 

 simplified theoretical models. Smith (1954), Gushing (1955) and Gushing and 

 Richardson (1955) have measured scattering cross-sections over limited 

 frequency ranges. At the moment we can only hope that such work will be 

 extended both to lower and higher frequencies. 



B. Scattering by Large Groups 



Volume scattering in the ocean is due to the contributions of many in- 

 dividuals. In some instances individuals can be resolved, especially when they 

 are close to source and receiver (see Fig. 5), but generally the observed volume 

 reverberation is a "smear" of the contributions arriving simultaneously from 

 many individuals. A common practice in volume-reverberation observations is 

 to use the same transducer both for projecting the sound and receiving the 

 returning reverberation. The transmission paths must be reciprocal for scatter- 

 ing from one object. Since it is commonly assumed that single scattering over- 

 whelmingly predominates, back-scattering is assumed to be measured when a 

 single transducer (or two very close together) is used. 



A convenient method of measuring scattering is to radiate the sound in a 

 succession of pulses each of which is short compared with the interval between 

 pulses. The transducer receives back-scattered energy between pulses which 

 has come from scatterers farther and farther from the source as time-after-pulse 

 increases. It seems unnecessary to describe in detail the apparatus employed 



1 The remarks in this paragraph are based on a study by Melvin Steinberg of the 

 University of Massachusetts (manuscript in preparation) who has studied the variation 

 of resonant frequency for a "free" jarolate spheroid, and also a "free" spheroid enclosed 

 in a thin, flaccid membrane. 



