SOUND PROPAGATION IN LIQUID CONTAINING MANY BUBBLES 



477 



and observation shown in Figures 5 and 6 is not bad. 

 Other runs show about the same agreement, with oc- 

 casional observed transmission losses as low as half 

 or as great as twice the predicted value, and with 

 occasional observed reflection coefficients as much as 

 6 db outside the spread of the observational data. 

 These discrepancies, which are apparently in random 

 directions, may be the result of irregularities in the 

 bubble-producing devices. It is worth noting that the 

 predicted scattering from nonresonant bubbles should 

 be quite reliable, since the theoretical values are in- 

 dependent of the damping constant. Hence it may be 

 concluded that the agreement of observations with 

 theory is within the observational error, and justifies 

 the practical use of the equations developed in this 

 chapter. 



Measurements on continuous-flow bubble screens 

 have also been described;' they showed relatively 

 poor agreement with the theoretical predictions. The 

 observed transmission losses rarely exceeded 25 db, 

 while the predicted transmission losses ranged be- 

 tween 50 and 200 db. It is doubtful whether such 

 great transmission losses could be observed, since 

 sound diffracted around the screen would be expected 

 to become important. In addition, in the continuous- 

 flow screen the smaller bubbles extended over a wider 

 region than the larger ones. At the lower supersonic 

 frequencies this halo of small bubbles would not 



absorb sound, but would reduce the sound velocity, 

 thus tending to bend the sound rays around the 

 screen. 



Furthermore, the predicted reflection coefficients 

 for the continuous-flow screen were some 5 to 15 db 

 greater than the observed values. The high specular 

 reflection predicted from theory for these continuous- 

 flow screens would presumably be reduced to a value 

 closer to the observed results if account were taken 

 of the absence of sharp boundaries. In view of the 

 many complexities entering into the explanation of 

 these measurements on the continuous-flow screen, 

 these discrepancies with theory may be disregarded. 



An important theoretical question which is not 

 answered by these experiments is the absorption pro- 

 duced by bubbles far from resonance. This non- 

 resonant absorption depends on the variations of S 

 with bubble radius and sound frequency. Since the 

 values of 8r are unexplained, the predictions of theory 

 as regards values of d under other conditions are of 

 little use. The bubble pulse measurements show that 

 the absorption by nonresonant bubbles is usually less 

 than about 5 per cent of the absorption by resonant 

 bubbles. It is not impossible that for some bubble 

 distributions present in wakes nonresonant absorption 

 might be practically important. Further observations 

 under controlled conditions would be required to 

 cast light on this point. 



