Application of the Mirror Source Method for Low Frequency Sound Prediction in Rectangular Rooms

The present study investigates the applicability of the mirror source method (MSM) to the prediction of the low-frequency modally dominated part of a room transfer function (RTF) in rectangular rooms with arbitrary, complex-valued boundary conditions on the room walls. It is known that the errors caused by application of the MSM with complex boundaries stem from the fact that the distances of sources, receivers to the boundary are not small compared to the wavelength. Thus, the study is focused on the 'practical' low frequency limit of the MSM. The study is based on the comparison of low frequency RTFs obtained from the mirror source and the finite element method (FEM), where the FEM results are considered as the reference. In order to allow the mirror source calculation up to very high orders, the study uses an efficient mirror source modeling algorithm for rectangular rooms which allows the assignment of individual frequency and angle dependent complex reflection factors to each of the six walls in the room. The simulation study focusses on four major aspects: (a) The quantification of the errors that are introduced by the mirror source approximation in the case of non-ideally rigid or soft walls as a function of frequency and average absorption in the room; (b) the simulation error due to the truncation of the MS calculation based on two different interrupt criteria (fraction of reverberation time and attenuation of mirror sources); (c) The impact of commonly applied simplifications of representations of the boundary conditions in the MSM (e. g. negligence of angle dependence of the reflection factor, negligence of the phase of the reflection factor) and (d) the influence of the proportions of the rectangular rooms. The presented results show that for moderately damped rectangular rooms of variable proportions the MSM provides a good approximation of the sound field already with reasonable reflection orders, if frequency and angle-dependent complex reflection factors are applied. The errors in narrow bands are typically below 1 dB in the frequency range above roughly once or the twice the Schroeder frequency but an increasing error in flat and long rooms is observed.