III-IO 



Using the orthogonality of the Legendre functions over the surface S, 

 we find from (III- 13): 



k^a = 



(2m + 1) 



(1 + C^) 

 m=0 ^ 



E 



(III- 17) 



The quantity n is a measure of the fraction of incident power diverted from the 

 original wave by the scatterer. The product (H • A) gives the total scattering 

 cross section of a sphere whose geometric section is A units. Because of the 

 complexity of the terms, it is not possible to do much further analysis with the 

 mathematical expressions. However, Anderson has computed values of Rq _ q 

 (backward scattering) and 11 for many cases. Figure III-l shows the value of 

 R/(ka)^ for various choices of relative density and sound velocity when 

 ka < < 1, and corresponds to (III- 15). 



THE QUANTITY R/(ka)^ IS 

 PRESENTED AS A FUNCTION 

 OF THE RELATIVE DENSITY g, 

 AND THE RELATIVE SOUND 

 VELOCITY h OF THE SCATTERING 

 SPHERE. 



FIGURE III-l RAYLEIGH SCATTERING FROM SMALL FLUID SPHERES 



IN THE BACKWARD DIRECTION (AFTER ANDERSON) 



As g and h both become small, R increases to „ , 2 . This happens when both 

 ° 3gh 



the density and the speed of sound decrease in the scattering sphere. As g and 



h become large, the situation compares to an incompressible fixed sphere and 



R - I (ka)^ . 



artbur B.littlcJnf. 



S-7001-0307 



