Abstract
In social environment there are various kinds of sound fields emitted by randomly distributed acoustic sources. In our previous paper we studied a flow of random acoustic point sources moving on a straight line as a simple model of road traffic noises, and derived space and time correlation of acoustic power observed at different points in the radiatted sound field. To begin with, in the present paper, simple approximate expressions for probability densities of PWL observed at a point surrounded by random distribution of point sources were derived by using the law of distribution of the nearest acoustic sources neighbor. The probability distributions are given in Eqs. (2. 11)〜(2. 13) and shown in Fig. 1. These curves make a parallel shift to the higher level side with an increase in the average density of point sources. These relations are given in Eqs. (2. 14)〜(2. 16). Especially Eq. (2. 14) for linear random array of point sources is in good agreement with the experimental formula representing the relation between a noise level near a road and trafic volume. Effects of an ambient background noise on the probability distributions of a direct sound were also studied and are shown in Fig. 2. It has been confirmed that a background noise usually has a great influence on the lower level side and raises a lowest level, but has little influence on the higher level side. Next we derived an accurate expression for the probability distribution of PWL observed at a point on a linear random array of acoustic sources. The results are compared with those of the approximate expressions mentioned above and shown in Fig. 3. When an observation point is not on a linear random array of sources as shown in Fig. 4, an approximate expression for the probability density of power transmitted to the point was also derived using the saddle-point method. The results are shown in Fig. 5. These statistical considerations on sound fields emitted by random distribution of point sources are considered to be usefull for estimation and physical understandings of traffic noises etc.
