Acoustical filters in plane‐wave fields

Abstract

Lumped‐parameter acoustical filters were thoroughly described by Warren P. Mason in his book on electromechanical transducers and wave filters. Today, the filtering action of open‐ended circular (standing‐wave) tubes and of plane‐parallel waveguides is described. The description is most simply in terms of the spatial wave fields of open‐ended tubes and slots. These were first analyzed accurately by L. A. Weinstein (Vaynshteyn) in the 1940s–1950s for both acoustical and electromagnetic waves. The basic mathematical technique was detailed examination of the diffracted field as a wave emerged from the open end after propagation inside the waveguide. The solutions to the diffraction problems are applied, in acoustical engineering, to the accurate analysis of open resonators, as well as to the analysis of probe tubes used for measurement of sound fields. Earlier investigators had been able to do no more than arrive at rough approximations in the form of “end corrections” to the length of a resonating circular tube, fianged at its open end.