Abstract
Abstract
In this chapter, solutions to the wave equation that satisfies the boundary conditions within three-dimensional enclosures of different shapes are derived. This treatment is very similar to the two-dimensional solutions for waves on a membrane of Chap. 10.1007/978-3-030-44787-8_6. Many of the concepts introduced in Sect. 10.1007/978-3-030-44787-8_6#Sec1 for rectangular membranes and Sect. 10.1007/978-3-030-44787-8_6#Sec5 for circular membranes are repeated here with only slight modifications. These concepts include separation of variables, normal modes, modal degeneracy, and density of modes, as well as adiabatic invariance and the splitting of degenerate modes by perturbations. Throughout this chapter, familiarity with the results of Chap. 10.1007/978-3-030-44787-8_6 will be assumed. The similarities between the standing-wave solutions within enclosures of different shapes are stressed. At high enough frequencies, where the individual modes overlap, statistical energy analysis will be introduced to describe the diffuse (reverberant) sound field.
Publisher
Springer International Publishing
Reference37 articles.
1. L.P. Eisenhart, Separable systems in Euclidean 3-space. Phys. Rev. 45(6), 427–428 (1934)
2. P.M. Morse, Vibration and Sound, 2nd edn (McGraw-Hill, New York, 1948), p. 396. Reprinted (ASA, 1981). ISBN 0-88318-876-7
3. B.F.G. Katz, E.A. Wetherill, The fall and rise of the Fogg art Museum lecture hall: A forensic study. Acoust. Today 3(3), 10–16 (2007)
4. L. L. Beranek, Concert and Opera Halls: How they Sound (Acoustical Society of America, New York, 1996); ISBN 1-56396-530-5
5. L.L. Beranek, Concert hall acoustics: Recent findings. J. Acoust. Soc. Am. 139(4), 1548–1556 (2016)