Series expansion for the sound field of a ring source

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.