Asymptotic modal analysis for sound fields of a reverberant chamber
Asymptotic modal analysis (AMA) has been applied to the sound fields of a reverberant chamber under narrow-band excitation by point sources. The result in the form usually given by geometrical acoustics also has been obtained by studying the asymptotic behavior of the result of wave or normal mode theory. A few numerical examples for a rectangular chamber are carried out to illustrate the way in which the asymptotic limit is approached. It is shown that the accuracy of the results depends on the number of modes in a frequency band of interest, the source position, and the chamber shape. A supplementary expression to improve the accuracy of the asymptotic theory has been derived for the case of a flat room, in which case the conventional geometrical acoustics type result is less accurate. The spatial distribution of the (mean-square) sound pressure also has been discussed. It is shown that, asymptotically, the sound pressure at all points of the chamber becomes the same except for some special regions, and that a large sound pressure appears at those exceptional regions. The regions near the walls and near the lines through the source perpendicular to the walls are special.
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