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Advances in Acoustics and Vibration
Volume 2014 (2014), Article ID 284362, 7 pages
Research Article

A Mathematical Images Group Model to Estimate the Sound Level in a Close-Fitting Enclosure

Mechanical Engineering, Gannon University, 109 University Square, Erie, PA 16541, USA

Received 11 January 2014; Revised 9 May 2014; Accepted 21 May 2014; Published 12 June 2014

Academic Editor: Andrew Peplow

Copyright © 2014 Michael J. Panza. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper describes a special mathematical images model to determine the sound level inside a close-fitting sound enclosure. Such an enclosure is defined as the internal air volume defined by a machine vibration noise source at one wall and a parallel reflecting wall located very close to it and acts as the outside radiating wall of the enclosure. Four smaller surfaces define a parallelepiped for the volume. The main reverberation group is between the two large parallel planes. Viewed as a discrete line-type source, the main group is extended as additional discrete line-type source image groups due to reflections from the four smaller surfaces. The images group approach provides a convergent solution for the case where hard reflective surfaces are modeled with absorption coefficients equal to zero. Numerical examples are used to calculate the sound pressure level incident on the outside wall and the effect of adding high absorption to the front wall. This is compared to the result from the general large room diffuse reverberant field enclosure formula for several hard wall absorption coefficients and distances between machine and front wall. The images group method is shown to have low sensitivity to hard wall absorption coefficient value and presents a method where zero sound absorption for hard surfaces can be used rather than an initial hard surface sound absorption estimate or measurement to predict the internal sound levels the effect of adding absorption.