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A power conservation approach to predict the spatial variation of the cross-sectionally averaged mean-square pressure in reverberant enclosures

Publication ,  Journal Article
Franzoni, LP
Published in: Journal of the Acoustical Society of America
December 29, 2001

Although it is commonly assumed that broadband mean-square pressure levels are spatially uniform in reverberant enclosures, there is a gradual spatial variation, especially if the room is long in one direction, and/or the acoustic absorption is not applied uniformly to the enclosure boundaries. An equation for predicting the average cross-sectional sound pressure levels in a lightly damped enclosure with absorption is derived based on conservation of acoustic power. The derivation involves a one-dimensional boundary value problem, the solution of which is an estimate of the average sound pressure level at cross-sections in the interior. In its simplicity, the resulting formula is reminiscent of the classical Sabine formulation; however, this prediction contains a spatially varying function that depends upon the distribution of absorption (side-wall versus end-wall). The formula is demonstrated on a model problem consisting of a rectangular acoustic enclosure with a source on one end-wall, absorption on the opposing end-wall, and a combination of hard and absorbing side-walls. Comparisons with an exact numerical simulation show that the prediction works well for a wide range of absorption levels and provides an improvement over classical diffuse field theory, where the levels are assumed to be spatially uniform. A formula for the volume-averaged, broadband, mean-square pressure (a modified Sabine formula) is also derived and shown to give excellent agreement with the numerical simulations. © 2001 Acoustical Society of America.

Duke Scholars

Published In

Journal of the Acoustical Society of America

DOI

ISSN

0001-4966

Publication Date

December 29, 2001

Volume

110

Issue

6

Start / End Page

3055 / 3063

Related Subject Headings

  • Acoustics
 

Citation

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Chicago
ICMJE
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Franzoni, L. P. (2001). A power conservation approach to predict the spatial variation of the cross-sectionally averaged mean-square pressure in reverberant enclosures. Journal of the Acoustical Society of America, 110(6), 3055–3063. https://doi.org/10.1121/1.1409538
Franzoni, L. P. “A power conservation approach to predict the spatial variation of the cross-sectionally averaged mean-square pressure in reverberant enclosures.” Journal of the Acoustical Society of America 110, no. 6 (December 29, 2001): 3055–63. https://doi.org/10.1121/1.1409538.
Franzoni, L. P. “A power conservation approach to predict the spatial variation of the cross-sectionally averaged mean-square pressure in reverberant enclosures.” Journal of the Acoustical Society of America, vol. 110, no. 6, Dec. 2001, pp. 3055–63. Scopus, doi:10.1121/1.1409538.

Published In

Journal of the Acoustical Society of America

DOI

ISSN

0001-4966

Publication Date

December 29, 2001

Volume

110

Issue

6

Start / End Page

3055 / 3063

Related Subject Headings

  • Acoustics