ランダムな平面波および球面波を用いた不規則音場モデルに関する統計的考察

抄録

In our acoustical environment there are various sound fields which are quite complex or essentially non-deterministic. In order to investigate the properties of these sound fields it is often convenient to consider their stochastic models composed of random wave elements. First we consider a stochastic sound field composed of many plane monochromatic wave elements. Rayleigh distribution is derived for probability density of pressure amplitude when the phases of plane wave elements are purely random. But this distribution is not necessarily dependent on the nature of wave number vector (i. e. direction of propagation) of each plane wave element. If we are concerned with diffusion of sound, therefore, it may be more rational to investigate the stochastic behaviors of particle velocity and flow of acoustic energy in the field, because they are also positively dependent on the direction of propagation of each component wave. Probability densities of them are derived when the wave number vector of each component wave is purely random in one-, two- and three-dimensions respectively. Especially the Maxwell distribution is obtained for the probability density of flow of acoustic energy in the three-dimensional case. These results are shown in Figs. 1 and 2. Covariance matrix for particle velocity at two points in the random sound field mentioned above is also derived and shown in Fig. 5. To express the random structure of the field, this tensor quantity may be more preferable than the usual correlation coefficient (i. e. scalar quantity) for sound pressure. The latter us obtained by simply averaging the former tensor elements. Then the flow of acoustic energy is investigated in a sound field emitted by a random distribution of acoustic point sources. Probability density of the flow is given by the Holtsmark distribution which is known well in stellar dynamics and shown in Fig. 6. Some remarks on a relationship between this and Maxwell distributions are also mentioned.