III-23 



We note that in the range of frequencies from 100 to 10, 000 cps, the 

 bubbles which are resonant will have radii between 0.03 cm and 3 cm. This coin- 

 cides with the range of bubble size most commonly found in the ocean. It is ap- 

 parent from Figure III-7 that within this range of frequencies, the expression 



f - TT— \ — — — is a very good prediction of the resonant frequency. 



The damping constant 6 , on the other hand, may be expected to depend 

 very heavily on the dissipative mechanism. We show in Figure III- 8 how the 

 damping constant 6 varies as a function of frequency for four typical bubbles . 

 These curves were computed according to Model III for the bubbles whose radii 

 and correspondmg resonant frequencies (at sea level) are indicated below. 



Radius (cm) f^ - Resonant Frequencies (cps) 



1.0 326 



0.1 3,240 



0.01 31,000 



0.001 260,000 



We have shown on each curve the frequency at which the bubble is resonant. Near 

 these resonant frequencies the dissipative and radiative mechanisms combine to 

 produce a minimum value of 6 . In other words, the contribution of the dissipative 

 mechanism to 6 decreases with increasing frequencies. The contribution of the 

 radiative mechanism to 6 increases with increasing frequencies, and both con- 

 tributions are important in the neighborhood of the resonant frequency since they 

 conspire to produce a minimum in that range. 



The damping constant has been studied extensively under a wide range 

 of frequencies and by means of several different experimental techniques. One 

 commonly used technique involves measuring the amplitude of the scattered wave 

 for various frequencies of the incident wave. The logarithmic decrement is then 

 given by 



A = TT- 



where f is the resonant frequency (maximum amplitude) and Af is the difference 

 of the two frequencies at each of which the response is one half of its maximum. In 



the literature, experimental results are expressed in terms of either A or 6 ; 



in this report all values are converted to 6 . 



artbur a.ltttleJnc. 



S-7001-0307 



