Effects of source and receiver locations in predicting room transfer functions by a phased beam tracing method

Abstract

The accuracy of a phased beam tracing method in predicting transfer functions is investigated with a special focus on the positions of the source and receiver. Simulated transfer functions for various source-receiver pairs using the phased beam tracing method were compared with analytical Green's functions and boundary element solutions up to the Schroeder frequency in simple rectangular rooms with different aspect ratios and absorptions. Only specular reflections were assumed and diffraction was neglected. Three types of error definitions were used: average error level over a narrow band spectrum, average error level over a 1/3 octave band spectrum, and dissimilarity measure. The narrow band error and dissimilarity increased with the source-to-receiver distance but converged to a certain value as the reverberant field became dominant. The 1/3 octave band error was found to be less dependent on the source-receiver distance. The errors are increased as the aspect ratio becomes more disproportionate. By changing the wall absorption from 0.2 to 0.8 for a rectangular room, the average narrow and 1/3 octave band error are deviated by around 1.5 dB. A realistic nonuniform distribution of the absorption increases the error, which might be ascribed to wave phenomena evoked by the impedance-discontinuous boundary.

Absorption and impedance boundary conditions for phased geometrical-acoustics methods

“…For example, a narrow band transfer function calculation from 20 Hz to 1 kHz at 2 Hz intervals of a 1000 m 3 room, employing 8000 beams up to the 100th specular reflection order, takes 1.5 h, while a boundary element calculation takes 56.5 h. 3 The advantage in terms of the calculation cost becomes significant as the room becomes larger and the upper frequency limit gets higher. An important advantage over the geometrical acoustics methods is flexible boundary modeling.…”

“…[1][2][3] Generally speaking, wave based methods are the most reliable methods in calculating transfer functions at low frequencies, whereas the geometrical acoustics methods provide approximate but reliable and fast predictions at frequencies well above the Schroeder frequency where room modes are highly overlapped; thus individual modal characters do not need to be taken into account. In this sense, the phased geometrical acoustics methods are normally considered as medium frequency methods that can bridge between low and high frequency methods.…”

“…A recent publication supports that the accuracy of a phased geometrical acoustics turns out to be acceptable even below the Schroder frequency, having a maximum error of 3 dB for a disproportionate room. 3 Therefore the phased geometrical acoustics methods can be alternatives to the wave-based methods in the acoustic simulations of small spaces such as car cabins, small class rooms, and meeting rooms as long as there is no significant effect of diffracting objects.…”

“…It has been reported that phased geometrical acoustics simulations using surface impedances as boundary conditions agree well with measurements and reference calculations. [1][2][3] Suh and Nelson used surface impedance boundary conditions for important surfaces to estimate the plane wave reflection coefficients, whereas real-valued angle-independent reflection coefficients are used for concrete and plaster walls, assuming no phase shift on reflections from these reflective surfaces. coefficients in a phased image source model in comparisons with boundary element simulations and geometrical acoustic simulations.…”

“…Jeong and Ih also used impedance boundary conditions for a phased beam tracing model in comparison with boundary element simulations and acoustic Green's function calculations. 3 The normal incidence specific surface impedance (f nor ) is a typical boundary condition in the phased beam tracing as well as the boundary element simulation. The use of f nor implies that the absorber is of local reaction because the surface impedance is assumed to be constant over the angle of incidence.…”