Consideration of Wall Reflection and Diffraction in the Room Acoustic Prediction Using the Phased Beam Tracing Method

The geometrical acoustics methods have been used to simulate the acoustics of rooms at high frequencies whereas the wave based methods have been devoted to calculate the low frequency response. The modified method, so called phased geometrical acoustics technique, was suggested for the extension of the applicability of the geometrical methods to mid frequency. Several studies on this method have demonstrated a good possibility to analyze the sound field in an enclosure at mid frequency. In this study, further considerations on wall reflection and diffraction have been investigated. The main suggestions are the use of approximated reflection coefficient and the integration with the theory of diffraction. This study aimed to improve the precision of the present method in mid frequency range and extend the applicability to the low frequency below Schroeder cutoff frequency. Because this method is originated from the geometrical acoustics, the wave‐particle duality can be discussed by comparing with result from modal method. The calculation parameters were thoroughly investigated. The number of beams and the frequency resolution were proved to be the most important parameters in the analysis and consequently the guidelines were suggested for these parameters. The approximate angle‐dependent/independent reflection coefficients were tested. The angle dependent reflection coefficient can take the angle dependence of the incident wave into account as well as the size effect of the surface. Also, the merit of representing the negative real part was discussed. The PBTM result shows a good agreement with the measurement especially in the early part of impulse response and at mid frequency. The new method of ii binaural simulation for the PBTM was suggested. The peculiar feature of frequency domain calculation of the PBTM gives advantages in the binaural simulation. Particularity in the early part of the impulse response at mid frequency, the binaural simulation result shows an excellent correspondence with the measurement in the application of a conference room. The diffraction phenomenon was incorporated into the PBTM based on the uniform theory of diffraction for the low to mid frequency simulation. The diffraction of edge, which is the topmost problem in an enclosed space, was tested. The simulated results by combining the PBTM with UTD agreed well with the previous research. Besides, the measurement in an anechoic chamber agreed better with the combined method than the ordinary PBTM in 125 Hz octave band. The simulation of an enclosure having a diffracting edge validates the improvement by comparing with the BEM result. One actual concert hall was tested to simulate the diffraction at receivers under a balcony According to the result of PBTM, the PBTM can be a mid‐frequency method bridging the gap between the low frequency method and high frequency method for the acoustic simulation of an enclosure as a unified approach. Furthermore, when a proper technique such as uniform theory of diffraction is integrated into, the present method can even deal with the low to mid frequency range, which has been considered as the typical territory for the wave based methods for a long time. The capability of calculating a room transfer function enables this method to be used in the analysis, design, diagnosis and refinement of a space. Because the applicable frequency range was extended to low‐to‐mid frequency, the small‐to‐medium sized room can be dealt with, vise versa. Therefore a small space like vehicle cabin and aircraft cabin can be dealt with by the present method as well as a large performance spaces.