Ill -53 



Macpherson's experiments involved measurements of reflection and 

 attenuation through carefully controlled bubble screens having a large number 

 of bubbles of uniform size and spacing. Bubbles were generated in a laboratory 

 tank by electrolysis and had average radii of 0.008 to 0.025 cm, depending upon 

 the electrode used. For any particular experiment, the standard deviation of 

 the radius was approximately 7% of the mean. In a vertical plane, the screens 

 had the form of one or more, essentially two-dimensional, slowly rising lat- 

 tices. The lattice spacings ranged from about one bubble in 10 cm^ to 40 bub- 

 bles in 10 cm^ . Measurements were made for one- millisecond sound pulses 

 with angles of incidence equal to 0° and 45°. The isonified area was 15 cm^ . 



Theoretical values were calculated following the approach of Carsten- 

 sen and Foldy. None of the incoherent terms were considered. 



Figure III- 24a shows the measurements and expected values of attenua- 

 tion produced by a single bubble screen of approximately 4 bubbles per cm^ . As 

 can be seen, the agreement with the theoretically predicted curves is good. The 

 slight spread of the experimental points outside the theoretical curves is ascribed 

 to the small nonuniformity of the bubbles. Similar results were obtained with 

 other spacings. Macpherson measured the damping constant 6 at 30 kcps as 

 0.080 ± 0.003. This corresponds closely to the theoretical value of 0.082 and 

 contrasts sharply with the poor agreement obtained by Carstensen and Foldy. 

 Macpherson also mentions that the "frequency variation of 6 at resonance over 

 the range 15-40 kc, and the off- resonant behavior were in close agreement with 

 the theory." 



For theoretical evaluations with more than one screen, it is assumed 

 that the attenuation is strictly additive, with no interaction between the screens. 

 This is justified by the fact that the spacing between screens is of the order of 

 4 cm, which corresponds to a wide spacing of bubbles and is analogous to the 

 case in which the bubbles were widely spaced in the lattice. In this latter case, 

 it was seen that the bubbles could be treated as independent scatterers, and by 

 the same argument, the successive screens can be considered independently. 

 Figure III-24c shows the result of placing two screens of slightly different bub- 

 ble sizes one behind the other, separated by a distance of about 4 cm. As can 

 be seen, the condition for no interaction is upheld inasmuch as the attenuation 

 and phase shifts add algebraically. The steady state reflection measurements 

 were made on screens similar to those used for transmission. The results for 

 a screen of 4 bubbles per cm^ are shown in Figure III-25 and can be seen to 

 agree very well with the theory. 



To provide experimental justification for calculating the theoretical 

 curves from the coherent term only, some measurements were made to show 

 the presence of the incoherent wave system. It was possible to show that about 

 10 cm from a nearly resonant screen of 4 bubbles per cm^ the measured inten- 

 sity of the incoherent component was of the order of magnitude given by the 

 theory, namely about 12 db. Away from resonance or further away from the 

 bubble screen, it was not possible to detect this component at all. 



Arthur Sl.ILittkJnt. 



S-7001-0307 



