Sound radiation of a circular piston in the outlet of a finite hemispherical cavity of a finite inner impedance

This study deals with the problem of sound radiation by a vibrating circular piston embedded in the outlet of a thick hemispherical cavity. It is assumed that the inner surface of the cavity is of a finite acoustic impedance. The problem is solved by dividing all spaces into some spherical subregions with uniform solutions in the form of the spherical harmonics. It is necessary, therefore, to satisfy the mixed Robin-Neumann boundary conditions as well as the continuity conditions. This leads to a system of algebraic equations. The necessary coupling integrals are expressed in terms of some highly convergent expansion series. The configuration of the flat circular radiator with a hemispherical baffle can be set in such a way that the back-scattering is significantly reduced while the main beam achieves a high amplitude. It has been shown that when the radiation resistance reaches its local maximum, it can result in stronger back-scattering. (C) 2019 Elsevier B.V. All rights reserved.