. Acoustic scattering in the ocean. Project TRIDENT; Underwater acoustics; Sound-waves. 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 comput
. Acoustic scattering in the ocean. Project TRIDENT; Underwater acoustics; Sound-waves. 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 S-7001-0307. Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these illustrations may not perfectly resemble the original Meyer, R. F; Romberg, B. W; Arthur D. Little, Inc. Cambridge, Mass. : Arthur D. Little, Inc.
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