III-56 



Typical velocity measurements obtained in one series of experiments 

 are shown in Figure III- 26. Bubble sizes for this series varied appreciably; 

 however, no details are given. No information is given regarding the frequency, 

 but since all velocities are less than that of sound in pure water, we can infer 

 that the frequency was always less than the resonant frequency of any major frac- 

 tion of the bubbles . 



Comparisons are made with the predictions of the preceding theory 

 and Wood's theory. The latter states that the velocity in a bubbly mixture is 

 given by 



(^y=(--^)0--^) 



where v is the volume of air per unit volume of mixture, p^ and p ' are the 

 density of the water and gas, c is the sound velocity in water, and P is the 

 pressure (including atmospheric). The results agree well with both theories 

 and indicate that: 



(1) The phase velocity is relatively independent of the frequency 

 when the incident frequency is less than the resonant frequency of a significant 

 fraction of the bubbles. 



(2) The phase velocity depends strongly on v, the fraction of air in 

 the mixture, with the velocity c (in feet per second) being given roughly by 



c = 100 (lOv)^/^ 



The results of more carefully controlled experiments are shown in Fig- 

 ure III-27. Here, phase velocity and attenuation are plotted as functions of fre- 

 quency and are compared with theoretical values given by Equation III-38. The 

 calculations were based on a single average bubble size (r) and air concentra- 

 tion. No information on the variations in bubble size or air concentration was 

 given. The figures are in order of decreasing concentration and decreasing 

 bubble size. Each plotted point was obtained by averaging 2 to 14 separate de- 

 terminations. Each experiment was made with a single bubble size, except for 

 the experiment whose data are shown in Figure III-27d; this latter experiment 

 was made with a mixture of two bubble sizes. Static pressure variation is ac- 

 counted for by the separate theoretical curves for each mixture depth. 



:artbur m.littlcJnt. 



S-7001-0307 



