III-45 



actually a fairly sharply defined core of larger bubbles in the middle with a 

 gradually tapering distribution of smaller bubbles in the front and back. In the 

 case of attenuation, the equipment limitations make a good comparison of theory 

 and experiment difficult. 



The Laird and Kendig experiments were designed to confirm, if pos- 

 sible, the very high attenuations predicted by Foldy's theory. In order to elim- 

 inate the effect of a reflected beam, both the projecting and receiving trans- 

 ducers were placed in the bubble field and measurements were made for vari- 

 ous separations of the transducers. A bubbly medium with a 2- by 6- foot cross 

 section was produced by forcing air through a taffeta screen located 12 feet be- 

 low the surface of a lake. 



Measurements of the attenuation were made at frequencies ranging 

 from 2 kc to 16 kc, and with the transducers separated by 1-1/2, 3, 4-1/2, and 

 6 inches. Figure III- 18 illustrates the data obtained. The vertical lines repre- 

 sent maximum fluctuations and the horizontal mark is an estimated average. 

 The random fluctuations in the bubble distribution caused the attenuation to vary 

 by as much as 40 db over a 10 second interval. 



For each frequency, the attenuation (in db per inch) was obtained by 

 plotting the attenuation data for the various separations, with the separation 

 distance along the x-axis and the attenuation (in db) along the y-axis. If the 

 data lie along a straight line, then the attenuation follows an exponential law, 

 and the slope of the line gives the attenuation in db per inch, which is then in- 

 dependent of the separation. Laird and Kendig remark that the data did not lie 

 perfectly along a straight line and that a "certain amount of judgment" was used 

 in fitting the straight lines . 



The data were analyzed in terms of Model III, by a procedure parallel- 

 ing that of Carstensen and Foldy. Again, only the first coherent term was con- 

 sidered. The expected and observed attenuations are compared in Figure III- 19. 



The bubble screens contained many different bubble sizes; consequently 

 it was necessary to use the integral representations for the complex propagation 

 constant. The experimental data for bubble distribution, n(R), and bubble volume 

 ratio, u(R), were well fitted by the distributions shown in Figure III-20. These 

 give the modal value of the number of bubbles per cm as 0.89 and the bubble 

 volume ratio 4.5 • 10"*. The Poisson distributions were used in calculating the 

 necessary integrals. Note that the resonant frequency of the bubbles correspond- 

 ing to the maximum value of u (R) is 6 kc, while that for bubbles corresponding 

 to the maximum of n (R) is 8.8 kc . 



Arthur H.ILittbJnt. 



S-7001-0307 



