Determination of sound-field diffusion indices based on FMBEM incidence directivity analysis

Regarding the diffuseness of sound field, several indices and their measurement methods have been proposed in terms of isotropy of traveling waves. In this paper, we attempt to calculate two kinds of diffusion indices based on the incidence directivity analysis employing the fast multipole boundary element method (FMBEM). The directivity analysis is performed for steady-state sound fields in a rectangular room with changing the absorption condition of the walls. As for diffusion indices, the directional diffusion coefficient is determined from the deviation of directivity of sound intensity, while alternative isotropy indicator is calculated through the spherical expansion of the directivity. The numerical results show general tendencies that the former index is almost constant, whereas the latter index decreases with increasing the frequency. As a common tendency, it is confirmed that the indices become higher in a reflective room condition, and remarkable dips occur around the natural frequencies when absorbing walls are unevenly distributed. Moreover, concerning the receiving cell, the size of it has little effect on the indices. On the other hand, it is verified that the indices become higher with the receiving cell near the point source.