Simplified expansions for radiation from a baffled circular piston

Abstract

Computation of acoustic radiation from a baffled circular piston continues be an active area of investigation, both as a canonical problem and because of numerous practical applications. For time-harmonic radiation, exact series expansions are an attractive approach because they do not require numerical integration or limiting approximations. Here, series expansions due to Hasegawa, Inoue, and Matsuzawa [J. Acoust. Soc. Am. 74, 1044–1047 (1983); 75, 1048–1051 (1984)] are shown to reduce to simpler expressions suitable for numerical computations of piston fields in lossless and attenuative fluid media. For the region r⩾a, where a is the piston radius and r is the distance from the piston center, an exact solution is given by an series of spherical Hankel functions and Legendre polynomials with explicit, closed-form, position-independent coefficients. For the paraxial region w⩽a, where w is the distance from the piston axis, a second exact series expansion is valid for all axial distances z and reduces to the known analytic solution for w=0. These two expansions allow the radiated field to be computed at any point, with rapid convergence except for points near the circle bounding the piston. Example numerical results illustrate application of this method to ultrasonic sources.