On the use of the method of wave images to introduce students to acoustics

Abstract

A previous paper [Ginsberg, 2006, J. Acoust. Soc. Am. 119, 1954-1960] extended the d'Alembert solution of the one-dimensional wave equation to semi-infinite and finite length waveguides. The concept uses images of incident waves in order to describe reflection phenomena. Each image is algebraically related to an incident wave when the restriction to purely resistive terminations is met. The present paper extends the previous treatment from initial value problems to situations in which the particle velocity at a termination is specified. The discussion emphasizes the use of hand-drawn sketches as a method that will allow students at all levels to understand the basic processes of wave propagation and reflection. The number and complexity of the wave images is enhanced in a bounded waveguide, so simple numerical algorithms for evaluating the response of such systems also are discussed. The wave image technique is applied to a sequence of increasingly complicated systems. Suggestions are given regarding what material should be presented to students at various levels, and what students can be expected to garner from each case. The recommendation is that this solution method should be used to introduce students at all levels to basic acoustical phenomena.