Relationship between acoustic reflection and vibrational modes of elastic spheres

Abstract

The behavior of the solution to acoustic backscattering by elastic spheres in water expressed as a form function vs ka, relative to the normal modes of vibration of solid homogeneous elastic spheres is examined. Specific free modes of vibration are identified with significant changes in form function. The solution for spheres of tungsten carbide, aluminum, and brass are considered for values of ka as high as 28. Minima in the form function usually occur at or near frequencies at which sphere resonances occur. Form functions are examined which are computed from mixing rigid and elastic terms in the waveharmonic series. In this way it is possible to see the effect of an isolated mode of vibration on the form function that describes the backscattering. Calculated resonance widths as well as observed pulse decay times allow determination of analytical and experimental Q’s of isolated resonances. Subject Classification: [43]20.30, [43]20.60, [43]20.50; [43]40.20.