A boundary element method is formulated in terms of time-averaged energy and intensity variables. The approach is applicable to high modal density fields but is not restricted to the usual low-absorption, diffuse, and quasiuniform assumptions. A broadband acoustic energy/intensity source is the basic building block for the method. A directivity pattern for the source is derived to account for local spatial correlation effects and to model specular reflections approximately. A distribution of infinitesimal, uncorrelated, directional sources is used to model the boundaries of an enclosure. These sources are discretized in terms of boundary elements. A system of equations results from applying boundary conditions in terms of incident, reflected, and absorbed intensity. The unknown source power for each element is determined from this system of equations. A two-dimensional model problem is used to demonstrate and verify the method. Exact numerical solutions were also obtained for this model problem. The results show that spatially varying mean-square pressure levels are accurately predicted at very low computational cost.

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.

That the modal analysis method works well regardless of the amount of damping in the system, provided that modal coupling is included in the analysis, is shown. The soundfield produced by a vibrating piston in a tube with an absorptive end is calculated. An exact solution is compared to results computed by modal analysis with and without the inclusion of modal coupling. Recent published results, which did not include the effects of modal coupling, incorrectly concluded that discrepancies were due to limitations of modal analysis, rather than the uncoupling assumption.

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Based on computer simulations of sound fields in rectangular enclosures, important observations are made regarding sound pressure levels and the spatial variation of the broadband reverberant field. From these observations an empirical formula is deduced that describes the slow spatial variation of the broadband reverberant mean-square pressure in one lengthwise direction. Two room shapes were studied: an elongated rectangular enclosure and an almost cubic enclosure, both with broadband sound source(s) on an endwall. Source position, relative phasing of multiple sources, level, and placement of absorptive material were variables in the study. The numerical results for the spatially averaged mean-square pressure in the reverberant field were often not in very close agreement with values predicted from a traditional Sabine approach. The prediction was improved by accounting for the power absorbed on the first reflection and an approximate formula is given for this correction factor. The reverberant sound field is characterized by a gradual spatial variation in the direction away from the source. This spatial variation scales exponentially with the sidewall absorptivity, as demonstrated by the numerical simulations. An approximate emperical formula is shown to predict this spatial variation fairly well. The computer simulations showed elevated sound pressure levels at the enclosure boundaries, for all cases, and also in the interior, for sound fields excited by a single broadband source on an endwall. These intensification zones occur along a plane in front of the source and along a plane which corresponds to the reflection of the source, whether or not the source is on a line of symmetry.