Three-Dimensional Enclosures

  • Steven L. Garrett
Part of the Graduate Texts in Physics book series (GTP)


In this chapter, solutions to the wave equation that satisfies the boundary conditions in 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.  6. Many of the concepts introduced in Sect.  6.1 for rectangular membranes and Sect.  6.2 for circular membranes are repeated here with only slight modifications. These concepts include 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.  6 will be assumed. The similarities between the standing-wave solutions within enclosures of different shapes are stress ed. At high enough frequencies, where the individual modes overlap, statistical energy analysis will be introduced to describe the diffuse (reverberant) sound field.


Acoustic Pressure Sound Field Radial Mode Azimuthal Mode Reverberation Time 
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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Steven L. Garrett
    • 1
  1. 1.Pine Grove MillsUSA

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