Ill -64 



Another example is furnished by the swim- bladders of fish. A previous 

 section of this report considered the scattering of sound by air bubbles . For a 

 single bubble, the scattered intensity has a peak at the incident frequency f^ 

 given by (III-22), which may be rewritten as 



2rrf = - A 

 o a 1 



3YP„ 



^ (III- 39) 



where a is the radius of the bubble, p^ the pressure on the bubble and p^ is the 

 density of the water. The intensity of sound scattered in the ocean often has a 

 pronounced peak at some particular frequency; thus, there is strong reason to be- 

 lieve that the scattering is caused by gas-bubble scatterers. Likely candidates are 

 fishes having gas-filled swim-bladders. The swim-bladders are not generally 

 spherical in shape, but nevertheless the properties of spherical bubble scatterers, 

 as a function of hydrostatic pressure and bubble size, are a useful guide for specu- 

 lation about the size of the fish and their behavior during migration in depth. 



Suppose that the gas-filled swim-bladders are spherical in shape and be- 

 have acoustically like free bubbles. As the fish swims from a shallow to a deeper 

 depth, its bubble is compressed and its buoyancy decreases. Consequently, it may 

 take gas from solution in the water and increase the gas in its swim bladder to ad- 

 just its buoyancy on the way down. If it reacts to keep its swim-bladder the same 

 size, then its resonant scattering frequency will vary as p^^^ . As it returns to 

 shallow depth, it must then vent or absorb gas from the swim-bladder to maintain 

 approximately neutral buoyancy. A second possibility is that the fish allows its 

 bubble to compress and expand with descent and ascent. TTiis implies that the fish 

 can tolerate being heavy at maximum depth. Assuming constant temperature, 



TT - a'^ p is a constant, hence 1/a varies as p''^^, from which we have 



'r " \l) 



5/6 



(III- 40) 



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

 depth amount to considerable changes in temperature as well. Almost everywhere 

 the ocean temperature decreases with increasing depth below the isothermal layer. 

 The effect of temperature on 1/a is approximately as T" ^^^. Usually the tem- 

 perature change will have the effect of reducing the frequency change by a small 

 amount- -of the order of 2% for a temperature change of 20°C. 



artbur m.littlcJnir. 



S-7001-0307 



