SECT. 4] 



SOUND SCATTERING BY MARINE ORGANISMS 



517 



In the foregoing development, no account has been taken of dissipative 

 forces acting on the bubble. A development has been made which takes into 

 account both frictional forces and heat interchange between bubble and water. 

 The details of the theory do not concern us here. The result, which is developed 

 in detail by Devin (1959), is an expression for the relationship between as and 

 / which is similar to (20) except that 'ZttRJX is replaced by a more complicated 

 term, S, containing a frequency dependent term and a term expressing frictional 

 forces acting on the bubble as well as the term 'IttRJX. These have the effect of 



0.004 0.006 0.0080.01 



Fig. 12. Ratio of scattering cross-section to physical cross-section [log (cts/tt-R^)] of an 

 ideal bubble versus (27ri?/A)Po-- (From Nat. Def. Res. Council Div. 6, 1946, chapter 



28.) 



reducing the back-scattering cross-section of the bubble near resonance, but 

 otherwise have little effect on its scattering properties. Fig. 12 shows the 

 scattering cross-section of an ideal bubble as a function of 2ttRPq''^I\. As a 

 result of experimental verification, equation (19) is regarded as reliably pre- 

 dicting the resonant frequency of bubbles in the range from 1 to 50 kc/s. The 

 value of 8 at resonance, hr, computed from the theory mentioned above, has 

 been compared with values derived from experimental measurements on 

 bubbles in fresh water. Results are shown in Fig. 13, which is based on a more 

 detailed graph presented by Devin (1959). 



We are interested in sound scattering by bubbles not only because they are 

 found near the surface but also because, as we shall see below, we have found 



