Series expansion for the sound field of a ring source

TL;DR

This paper derives an exact series expansion for the sound field of a monopole ring source with angular variation, enabling precise calculations of radiated fields for various circular sources and their derivatives.

Contribution

It introduces a novel series expansion method for ring source sound fields, applicable to arbitrary circular sources and higher order derivatives, based on a prior finite disk field expression.

Findings

Series expansion accurately models ring source sound fields.

Method applies to arbitrary circular sources of finite extent.

Enables calculation of higher order source fields like dipoles and quadrupoles.

Abstract

An exact series expansion for the field radiated by a monopole ring source with angular variation in source strength is derived from a previously developed expression for the field from a finite disk. The derived series can be used throughout the field, via the use of a reciprocity relation, and can be readily integrated to find the field radiated by arbitrary circular sources of finite extent, and differentiated to find the field due to higher order sources such as dipoles and quadrupoles.