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.