518 



HERSEY AND BACKUS 



[chap. 13 



that many scattering layers exhibit strong resonant scattering, and have a 

 single resonant peak suggesting that they are made up of gas-bubble scatterers. 

 We shall see that the likely candidates are fishes having gas-filled swim- 

 bladders. The swim-bladders are not generally spherical in shape, but neverthe- 

 less the properties of spherical bubble scatterers, as a function of hydrostatic 

 pressure and bubble size, are a useful guide for speculation about the size of 

 the animals and their behavior during migrations in depth. 



Let us assume for the moment that gas-filled swim-bladders are spherical 

 and behave acoustically like free bubbles. As the fish swims from a shallow to 

 a deeper depth its bubble is compressed and its buoyancy will decrease. Con- 

 sequently it may well take gas from solution in the water and increase the gas 

 in its swim-bladder to adjust its buoyancy on the way down. If it reacts to 

 keep its swim-bladder the same size {R constant) then, from (18), its resonant 



0.20 



0.10 



S 0.04 



Q 



0.02 



10 20 40 



RESONANT FREQUENCY fn (kc/s) 



100 



200 



400 



Fig. 13. Theoretical curve and experimental values of total damping constant of resonant 

 air bubbles in water. The points are taken from the work of seven experimenters 

 using various methods of determination. (After Devin, 1959.) 



By courtesy of C. Devin, Jr., The George Washington University and The David 

 Taylor Model Basin. 



scattering frequency will vary as P'/^. Of course, as it returns to shallow depth 

 it must vent or absorb gas from the swim-bladder to maintain approximately 

 neutral buoyancy. Kanwisher and Ebeling (1957) point out that the swim- 

 bladders of migrating lantern-fishes, caught at the surface at night, have a 

 high percentage of oxygen, indicating that they have taken on oxygen at 

 depth. Nevertheless they regard it unlikely on physiological grounds that these 

 fishes maintain neutral buoyancy by changing their gas content during migra- 

 tion (see page 535). A second possibility is that the fish allows its "bubble" to 

 compress and expand with descent and ascent. (This assumption implies that 

 the fish can tolerate being "heavy" at maximum depth.) Under such an 

 assumption, the factor IjR in (18) varies as P'/», from which we may write 

 approximately 



fifo = (P/Po)^/« 



