Spherical Wave Radiation in Solid Media

Abstract

Divergent compressional waves in solids differ from similar waves in fluids, even though the particle displacement be parallel to the direction of propagation in both media. Perhaps the simplest example is the wave propagating from a radially oscillating spherical cavity in an infinite solid medium. When a sinusoidally varying pressure is generated in such a cavity, the normalized acoustic radiation impedance is a function of σ, the Poisson's ratio of the medium, as well as of the ratio of cavity radius to wavelength. As σ increases from zero to one-third, the radiation reactance varies in magnitude, but remains a negative or stiffness reactance at all frequencies. When σ becomes greater than one-third, a resonance frequency of zero radiation reactance appears, above which the reactance is positive or inertial. Then as σ approaches its limiting value of one-half, the resonance frequency decreases to zero and the familiar accession to inertia of fluid medium acoustics is obtained. When an impulsive pressure is generated in the cavity, as by an explosion, the form of the radiated pulse is a damped wave train which does not closely reproduce the original pressure pulse.