Acoustical Scattering from an Elastic Sphere in Water: Surface Wave Glory, Resonances, and the Sommerfeld-Watson Transformation for Amplitudes

摘要

Scattering of acoustic waves from fluid-load elastic spheres with 10 < ka < 100 (where k is the wavenumber of the acoustic wave in the liquid and a the radius of the sphere) is studied, The main emphasis is on understanding the scattered pressure near backscattering. By carrying out a Sommerfeld-Watson Transformation (SWT) it is shown that this pressure includes contributions from specular reflection, transmitted bulk waves, and surface waves. It is shown experimentally that surface wave contributions to near backscattering display a J sub o Bessel function angular dependence characteristic of weak axial focusing along the backscattered direction; i.e., glory scattering. This focusing is modeled by alternate methods which agree and complement each other. One method allows a simple picture of the glory phenomena while the others (which includes the SWT) are more mathematically rigorous. The absolute value of individual Rayleigh and whispering gallery surface wave contributions is found by this modeling. The theoretical results for are tested experimentally using the Rayleigh surface contribution to scattering from a tungsten carbide sphere. The SWT results are also used to find the far field backscattering pressure as a function of ka. These results are used to better understand and interpret the recently developed Resonance Scattering Theory (RST) as applied to acoustic scattering. It is shown that surface wave contributions to backscattering may be summed in a way analogous to the frequency response of a Fabry-Perot resonator.