Approximation to the Diffraction of Sound by a Circular Aperture in a Rigid Wall of Finite Thickness

Abstract

An approximate solution for the diffraction of a plane sound wave incident normally on a circular aperture in a plane rigid wall of finite thickness is obtained by postulating rigid, massless, infinitely thin plane pistons in each end of the aperture, whose motions simulate the movement of the air particles at these positions under acoustic excitation. Plane longitudinal waves are assumed inside the aperture. Numerical solutions obtained on an IBM-7090 computer very closely coincide over a wide range of frequencies with those of much more-complicated existing exact solutions. Furthermore, extensive experiments were conducted on the transmission of reverberant sound through steel pipes of various lengths and diameters inserted individually into a heavy wall between two concrete chambers of 1750 cu ft each. Measured values of reverberant sound-transmission loss through these apertures were found to agree within experimental error with those calculated from the approximate theory. The assumption of plane-wave propagation in the aperture was found to give valid experimental results up to values of d/λ exceeding unity, where d is the pipe diameter and λ is the wave length of incident sound.