Philip L. Marston
Dept. of Phys., Washington State Univ., Pullman, WA 99164-2814
Early calculations [L. Flax, J. Acoust. Soc. Am. 62, 1502--1503 (1977)] of the exact partial-wave series of elastic objects in water for ka from 900 to 950 suggest that elastic contributions to backscattering are relatively more important for spheres than for circular cylinders. The main distinction between the two situations is the axial symmetry of the sphere that produces backwards directed toroidal wave fronts associated with off-axis rays [P. L. Marston and L. Flax, J. Acoust. Soc. Am. Suppl. 1 68, S81 (1980)]. In addition to geometrical considerations and diffraction theory leading to a (ka)[sup 1/2] factor for such focusing, early support for this hypothesis was provided by calculations [L. Flax (personal communication, 1980)] for an aluminum sphere with ka=938 showing the form function magnitude |f| as a function of the backscattering angle (gamma)=(pi)-(theta). The enhancement of |f| is localized to small values of (gamma) as expected from the theory of axial focusing. The analysis of axial focusing [P. L. Marston, Physical Acoustics (Academic, New York, 1992), Vol. 21, pp. 1--234] is not limited to such extremely large values of ka and includes elastic shells and other symmetric objects. [Work supported by ONR.]