Calculation of amplitudes of acoustic normal modes from the reciprocity principle

Recently, J. D. Achenbach [J. Acoust. Soc. Am. 116, 1481-1487 (2004)] put forward, on heuristic grounds, an elegant technique to calculate amplitudes of guided waves in an elastic solid. The technique is based on application of the reciprocity principle. In this article, the technique is applied to acoustic waveguides. A mathematical justification of the technique is obtained. The technique is extended to enable calculation of excitation coefficients of modes of both discrete and continuous spectra by a given sound source. The results are shown to be identical to those derived with the traditional methods that rely on integral transforms.