On the spherical expansion for calculating the sound radiated by a baffled circular piston

Abstract

An efficient and accurate method for calculating the sound radiated by a baffled circular rigid piston is using spherical harmonics, and the solution is a series containing the integral of spherical Bessel functions. The integral is usually calculated with the generalized hypergeometric functions in existing literatures, which shows poor convergence at middle and high frequencies due to the overflow and the loss of significant figures. A rigorous and closed form solution of the integral is derived in this paper based on the recurrence method, which is accurate in the whole frequency range and thousands of times faster than the existing methods. It is shown that the proposed method can be extended for the calculation of the sound radiated by a baffled piston and an unbaffled resilient disk with axisymmetric velocity and pressure profiles, respectively, and some baffled rotating sources where the velocity profile is asymmetric.

A cylindrical expansion of the audio sound for a steerable parametric array loudspeaker

“…30 This can be regarded as the two dimensional version of the spherical expansion for the sound field radiated by a circular piston source. 18,31,32 The cylindrical expansion converges quickly because no integral with highly oscillatory integrand is required to calculate. In addition, the radial and angular coordinates are uncoupled (separated) so that they can be calculated quickly for many observation points.…”