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

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. 1. Introduction Many studies have been done on the insertion loss of enclosures including the effect of reverberant buildup inside enclosures as well as the sound transmission loss of the enclosure surfaces. As the focus of this paper is the internal sound field only, analytical studies relating, in some significant way, to this are considered. Tweed and Tree [1] focus on the insertion loss of the enclosure (i.e., difference in sound pressure level at the same position outside enclosure) and compare the prediction from Jackson [2], Junger [3], and Ver [4]. Each of these three studies considers a plane wave radiated by the noise source. Jackson [2] considers infinite wall panel sound transmission loss and Junger [3] considers a finite panel sound transmission loss. Ver [4] considers three frequency regions relative to panel fundamental natural frequency and the acoustic frequency of lumped air space between source and wall panel. Tweed and Tree [1] conclude that all three methods give differences large enough to cause concerns in accurate enclosure design. Osman [5] uses the diffuse field