直方体残響室における2点間音圧相関係数

抄録

In this paper, the correlation coefficient of sound pressure in a rectangular reverberant room is studied. The results of numerical calculations at lower frequencies are compared with the experimental ones, and the relation between the geometric acoustics and the wave theory is also mentioned. We consider the sound field in the room excited by narrow band noise. According to Morrow's assumptions, the mean (time-averaged) square pressure distribution along the Y-direction at (x_0, y, z_0) is given by Equations (1) and (3). Here, B^2_m is regarded as representing the directivity power spectrum along the Y-direction at (x_0, y, z_0). The directivity power spectro correspond to those of the traversing microphone spectra scopy. Following the Wiener-Khintchine's theorem with respect to the spatial correlation, it is expected that the correlation coefficient along the Y-direction at (x_0, y, z_0) is given by Equation (5) where B^2_m has been normalized. Here, assuming that B^2_m has an equally probable continuous distribution as shown by Equation (6), the Cook's formula is derived. But the equation (5) is not practical for a finite rectangular room, in particular, at lower frequencies, because, in general, we cannot expect the stationarity with respect to space. Therefore, the correlation coefficient between A(x_0, Y_A, z_0) and B(x_0, Y_A+Δy, z_0) is given by Equation (9) where B^2_m represent the directivity power spectra as stated above. The reverberant room in our laboratory is rectangular as shown in Fig. 1. A block diagram for the measurements is shown in Fig. 2. At 125 Hz (1/3 Oct. ) and 250 Hz (1/3 Oct. ), the theoretical results are compared with the experimental ones, as shown in Figs. 3-12. But the measurements of the directivity power spectra are not performed here. It seems that the condition of the sound source position is reflected those results, and these results correspond to the theoretical ones for the most part. Some practical examples that we can assume theoretically the correlation coefficients of sound pressure in a rectangular reverberant room, are shown here.