III-40 



Meyer and Skudrzyk made certain calculations of the expected at- 

 tenuation and phase velocities for sound passing through water interspersed 

 with air bubbles . For their calculations they used a damping constant given by 



6 = 



0.015 + 11x10"'= f 



where f is the resonant frequency of the bubble. This expression is based on 

 the experimental work of Meyer and Tamm; however it gives damping constants 

 which are larger than those given by other theories and found in other work, as 

 may be seen by comparison with Figure III-9. As a result, many of Meyer and 

 Skudrzyk' 8 theoretical attenuation figures may be too high. 



Figure III- 13a shows the theoretical sound damping (in db/cm) as a 

 function of the frequency, for a screen of gas bubbles which are all roughly the 

 same size and have a resonant frequency of 12 kc. The radii of the bubbles are 

 approximately 0.026 cm. The parameter is the relative gas content (by volume), 

 which, in this graph, ranges from 10 ^ to 10" ^ . The strongest damping takes 

 place at the resonant frequency. The curves are symmetrical for small gas 

 content and unsymmetrical for large; thus the higher frequencies are more 

 strongly influenced. The maximum damping is 0.3 db/cm at a gas concentra- 

 tion of 10'® and 95 db/cm at 10'^ . This means that for the first example ap- 

 proximately one air bubble occurs per 100 cm , while in the second case ap- 

 proximately 100 bubbles occur in 1 cm . 



Figure III- 13b shows the calculated phase velocity of the bubble- 

 water mixture for three concentrations, with the bubbles resonant at 10 kc. 

 The velocity in the bubble-free medium Cg was taken as 1400 meters/sec. 



An experimental screen of fairly uniform bubbles was created by 

 forcing air through a porous plate. The results of attenuation measurements 

 for such screens are shown in Figure III- 13c. A number of screens corre- 

 sponding to different volume concentrations were generated by varying the in- 

 put rate of air from 160 to 500 liters per hour. The resonant frequency of the 

 bubbles appears to be approximately 15 kc. The measured curves for the vari- 

 ous quantities agree qualitatively with the theoretical curve of Figure III- 13a. 



When the diameters of the gas bubbles are distributed over a sizable 

 range, we must use the integral form of the theory. As a special case, Meyer 

 and Skudrzyk consider a screen made up only of bubbles whose resonant fre- 

 quencies lie between 10 kc and 100 kc, i.e., bubbles whose radius lies between 

 0.033 cm and 0.0033 cm. In this band, the volume concentration, v, of the bub- 

 bles was taken to be constant; thus, there are very few large bubbles, but very many 

 small ones. Figure III- 14 shows the sound damping under these conditions, as 

 a function of frequency. 



Arthur M.lLxttltMt. 



S-7001-0307 



