Index of content:
Volume 103, Issue 4, April 1998
- ARCHITECTURAL ACOUSTICS 
A discussion of modal uncoupling and an approximate closed-form solution for weakly coupled systems with application to acoustics103(1998); http://dx.doi.org/10.1121/1.421344View Description Hide Description
Modal analysis is often used to solve problems in acoustics, leading to a system of coupled equations for the modal amplitudes. A common practice in analytical work utilizing modal analysis has been to assume that weak modal coupling is negligible, thereby enabling the modal coefficients to be solved independently in closed form. The validity of this assumption, as well as the order of the error from neglecting modal coupling, is discussed. It is possible to incorporate the principal effects of weak modal coupling in a very simple way without solving the fully coupled system. An approximate closed-form solution for weakly coupled systems of equations is developed. The procedure gives insight into the errors incurred when coupling is neglected, and shows that these errors may be unacceptably large in systems of practical interest. A model problem involving a pipe with an impedance boundary condition is solved when the one-dimensional sound field is harmonically driven, and when it undergoes reverberant decay from initial conditions. The approximate solution derived in this paper is compared with results for the fully coupled and fully uncoupled equivalent problems. The approximation works well even for systems where the coupling is fairly strong. The results show that modal coupling must be included, at least approximately, if certain salient features of the sound field, such as intensity flow and detailed reverberant structure, are to be predicted correctly.
103(1998); http://dx.doi.org/10.1121/1.421345View Description Hide Description
Simplified models for predicting noise levels in industrial workrooms have been developed by Friberg, Thompson et al., Wilson, Embleton and Russell, Kuttruff (“diffuse” and “specular” models applicable to fitted rooms only), Zetterling, Sergeyev et al. (applicable only to untreated workrooms), and Hodgson. They predict octave-band or A-weighted steady-state sound-pressure level as a function of source/receiver distance. These models have been programmed and evaluated by comparing predicted sound-propagation curves with those measured in 30 empty and fitted industrial workrooms with and without absorptive ceiling treatments. In empty workrooms the Sergeyev et al., Thompson, and Hodgson models worked quite well. The Zetterling model performed moderately well. The other models were inaccurate. Models underestimated levels in most cases. With the addition of absorbent treatments the accuracy of the Friberg, Wilson, Zetterling, and Embleton and Russell models improved; that of the Thompson and Hodgson models worsened. In fitted workrooms the Hodgson and Kuttruff (diffuse) models were accurate. The Friberg and Zetterling models were moderately accurate. The other models were inaccurate. The Thompson and Kuttruff (specular) models generally overestimated levels; the other models tended to underestimate levels. With absorbent treatment the accuracy of the Embleton and Russell model improved.