Sound penetration through a thin circular ring

Abstract

The penetration of sound through a circular ring-aperture in a rigid screen is investigated in the low frequency limit. The approximate solution for the relevant integral equations is found in the limit of a very thin ring. The solution, which is valid for arbitrary right-hand members, is applied to the integral equations which occur in the determination of the first three terms of the low frequency expansion. Special attention has been given to the transmission cross-section, which is of interest for the study of acoustical powerleakage through peripheral cracks. The results show good agreement with those obtained by numerical methods. Not taken into account are the influence of the frictional resistance at the edge of an imperfectly rigid screen and the non-linear effects of viscosity, which will render the normal velocity finite at the edges.