Losses Due to Bubbles 



A large amount of work has been done on the problem 

 of the sound attenuation introduced by bubbles. 4 ' x 9 ' 34 ' 43 ' 44 

 The most recent experimental evidence substantiates the 

 notion that the thermal, radiation, and viscous losses 

 adequately describe the attenuation of a bubble vibrating 

 close to its resonance frequency. * It is usually assumed 

 that the effect of bubbles much smaller than the resonance 

 size, corresponding to the measuring frequency, is very 

 small. However, the following discussion indicates that 

 this conclusion may not always be justified. 



When the glass rod in the captured bubble experiment 

 was moved around close to the center of the cavity, it was 

 found that the attenuation caused by the bubble was sub- 

 stantially constant provided that the bubble was within a 

 distance of approximately 2 cm from the center. Now 

 suppose the bubble is divided into many smaller bubbles 

 with the same total volume as the single bubble and dis- 

 tributed within 2 cm from the center of the cavity. It must 

 be expected that the resonance phenomenon is basically 

 unchanged. The attenuation caused by the air volume, 

 however, will have changed in a marked degree. The 

 reradiated sound will not contribute to the total loss by 

 cavity measurements, in accordance with the behavior of 

 the single bubble. The viscous losses will be the same or 

 perhaps somewhat larger, since the motion in the water is 

 essentially unchanged except in the immediate neighbor- 

 hood of the bubbles. The thermal losses will be consider- 

 ably smaller, since the air in the small bubbles will be 

 almost at the same temperature as the water throughout 

 a wave cycle. The thermal loss of a resonant bubble 

 arises if the disturbance of the gas is neither adiabatic 

 nor isothermal; in this case there must be a phase differ- 

 ence between the acoustic pressure and the particle velocity. 



''^Private communication from Dr. D. E. Andrews, NEL. 



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