Benchmark analytical solutions for steady state high frequency broadband sound fields in three rectangular enclosures.

Analytical solutions are presented for broadband sound fields in three rectangular enclosures with absorption applied on the floor and ceiling, rigid sidewalls, and a vertically oriented dipole source. The solutions are intended to serve as benchmarks that can be used to assess the performance of broadband techniques, particularly energy-based methods, in a relatively straightforward configuration with precisely specified boundary conditions. A broadband Helmholtz solution is developed using a frequency-by-frequency modal approach to determine the exact band averaged mean-square pressures along spatial trajectories within each enclosure. Due to the specific choice of enclosure configuration and absorption distribution, an approximate specular solution can be obtained through a summation of uncorrelated image sources. Comparisons between the band averaged Helmholtz solution and the uncorrelated image solution reveal excellent agreement for a wide range of absorption levels and improve the understanding of correlation effects in broadband sound fields. A boundary element solution with diffuse boundaries is also presented, which produces consistently higher mean-square pressures in comparison with the specular solution, emphasizing the careful attention that must be placed on correctly modeling reflecting boundary conditions and demonstrating the errors that can result from assuming a Lambertian surface.

An angle-by-angle approach to predicting broadband high-frequency sound fields in rectangular enclosures with experimental comparison.

Experiments were performed on an elongated rectangular acoustic enclosure with different levels of absorptive material placed on side walls and an end wall. The acoustic source was a broadband high-frequency sound from a loudspeaker flush-mounted to an end wall of the enclosure. Measurements of sound-pressure levels were averaged in cross sections of the enclosure and then compared to theoretical results. Discrepancies between the experimental results and theoretical predictions that treated all incidence angles as equally probable led to the development of an angle-by-angle approach. The new approach agrees well with the experimentally obtained values. In addition, treating the absorptive material as bulk reacting rather than point reacting was found to significantly change the theoretical value for the absorption coefficient and to improve agreement with experiment. The new theory refines an earlier theory based on power conservation and locally diffuse assumptions. Furthermore, the new theory includes both the angle of incidence effects on the resistive and reactive properties of the absorptive material, and the effects of angle filtering, i.e., that reflecting waves associated with shallow angles become relatively stronger than those associated with steep angles as a function of distance from the source.