What is it about?
Rigid disks approximate the operation of electrodynamic loudspeakers and resilient disks approximate the operation of electrostatic loudspeakers. The use of spherical coordinates is a standard approach to calculating the sound pressure and the paper treats both cases in a similar framework, and presents results in a consistent form.
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Why is it important?
Spherical expansions for radii less than the disk radius produce poor convergence. The paper uses a small argument approximation of the product of a spherical Bessel and spherical Hankel function to show that, for both cases, the high order expansion terms can be simplified which allows part of the solution to be evaluated to infinity. This reduces the expansion error to similar levels of other (paraxial) solutions.
Perspectives
The low-frequency solutions are "edge-wave" solutions, eg the sound field due to a rigid disk of radius a can be viewed as the solution for an oscillating infinite plane, minus the sound field produced by an infinite oscillating plane with a fixed rigid disk of radius a. Thus, the low-frequency solution (52) for r < a has a plane wave term and a second term which is the low-frequency solution of the plane with rigid disk. The plane wave term is the part that results from the infinite expansion and which reduces the error.
Mark Poletti
Callaghan Innovation
Read the Original
This page is a summary of: Spherical expansions of sound radiation from resilient and rigid disks with reduced error, The Journal of the Acoustical Society of America, September 2018, Acoustical Society of America (ASA),
DOI: 10.1121/1.5054010.
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