A new theory for the radiation from a concave piston source

The exact theory for the radiation of a circular concave piston surrounded by an infinite rigid baffle is presented. The Rayleigh surface integral, giving the velocity potential for a circular concave piston source, reduces to an infinite series of the simplest form when the origin of a system of spherical coordinates is taken at an arbitrary point on the acoustic axis. The theoretical framework has the advantages that it includes neither approximations nor numerical integrations and that it has application in solving other boundary‐value problems such as the sound scattering by a sphere whose center coincides with the origin in the field of a concave piston source.