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

TLDR

An approximate diffraction model treats the aperture ends as rigid, massless pistons and assumes plane longitudinal waves inside, and is validated by experiments on steel pipes inserted in a heavy wall. Numerical results closely match exact solutions over a wide frequency range, and experimental measurements of reverberant sound‑transmission loss through steel pipes agree with the theory, confirming the plane‑wave assumption up to d/λ ≈ 1.

Abstract

An approximate solution for the diffraction of a plane sound wave indicent 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 ft3 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. Experimental results indicated that the assumption of plane-wave propagation in the aperture was valid up to values of d/λ exceeding unity, where d is the pipe diameter and λ is the wavelength of incident sound.