Abstract
A rigid prolate spheroidal obstacle that is part of a mass-spring-dashpot system in an acoustical medium is struck by a plane pressure wave and also by a spherical pressure wave. ZP* (k) and ZS* (k) are the Fourier transforms of the motion of the spheroid in the plane-wave case and spherical-wave case, respectively, and f* (k) and g* (k) are the respective transforms of the incident pressures in these cases. The equation relating ZP* (k) and f* (k) and the equation relating ZS* (k) and g* (k) are derived. The asymptotic forms for the acoustical admittances ZP* (k)/f* (k) and ZS* (k)/g* (k) are computed for k small and from these results the condition that f and g must satisfy in order that ZP (t)∼ZS (t) for t large is derived. Finally the distance c between the foci of the spheroid is allowed to approach 0, yielding the preceding results in the case of a spherical obstacle.
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