半無限障壁による回折音場

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In predicting and controlling the propagation of noise in the open air, it s very important to take account of the shape of a building that is the noise source, the cross sections of railway track and road, as well as barriers and surrounding buildings. Then, the theory of the free-field diffraction of a spherical sound wave by a thin half-plane is basically necessary. The early approximate diffraction theories of Fresnel and Kirchhoff are well known, where it is supposed that the linear dimensions of the opening are large compared with the wave-length and the diffracting plane is perfectly absorbent. The rigorous solution of a diffraction problem of a plane wave incident on a thin half-plane was first given by A. Sommerfeld. On the basis of his solution H. S. Carslaw solved the three-dimensional case of a spherical wave, and H. M. Macdonald gave a useful form of the exact solution. However, Maekawa's experimental curve is often used for the calculation of noise reduction of a barrier, which is obtained by experiment to satisfy the Kirchhoff's approximate condition. This paper makes clear the behavior of Macdonald's exact solution by a numerical calculation which seems to have been surprisingly unknown, and presents detailed data of experiments, many of which do not satisfy the Kirchhoff's approximate condition. The theoretical and experimental results are shown in Figs. 2-13 as follows: 1) According to the Macdonald's exact solution there is a contribution of image source to diffraction, and sound attenuation by a screen ATT. is given by three normalized distance parameters, namely, R_N, distance normalized by a half wave-length from the point of observation to the source; R^^_N, to the image source, and R_<1N>, over the edge of the half-plane to the source. 2) The Kirchhoff's approximate solution is in agreement with the expression where the contribution of image source is neglected and R_<1N>≃R_N in the exact solution. 3) All of the experimental results are in very good agreement with the exact solution, no matter where the sound source and the point of observation are located. 4) The Maekawa's experimental curve deviates largely from the experimental results and the exact theoretical results when either the source or the point of the observation is comparatively near the half-plane. 5) By the useful simple approximate expression of the exact solution which is accurately given by Bowman & Senior, the approximation error is less than 0. 5dB only if λ/4<R_1, here R_1 is the minimum distance from the point of observation over the edge of the half-plane to the source. Consequently, we can predict and control the propagation of noise in the open air very accurately by applying the Macdonald's exact solution or that approximate expression.
社団法人日本音響学会の論文
1976-05-01

半無限障壁による回折音場

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