音の伝搬に対する風速分布の影響
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概要
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Wind speed distribution plays an important role on the propagation of sound outdoors. Hitherto, its effects have been explained unsatisfactorily by sound ray and shadow zone theory. The author proposes new method of caluculation which is based on Fresnel's theory in optics and the phase change of sound waves by wind. If there is no wind, Fresnel's theory says that sound field at R(Fig. 1) can be calculated by integrating secondary waves from the surface elements on the reference sphere. Lunar portion (Fresnel's lune in Fig. 2) can be taken as the surface element, then wave element is given as eq. (1). Integration of eq. (1) makes Cornu's spiral(Fig. 3), from which wave field at R can be determined. If there is wind speed distribution, it is assumed that the wave element from the lunar portion becomes the form of eq. (2), which means wind affects only on the phase of secondary waves and not on the amplitude. This is based on the idea that wind speed is small as compared with sound speed, so that wind effect should be small. But the phase change is accumulated with distance, therefore the effect of wind on the phase should not be ignored in long distance. Integration curve of eq. (2) is shown in Fig. 5, in which wind distribution is assumed as w_0(x/x_0)^<0. 33>, and the reference sphere is divided into 1 cm step from 0 to 20 m height. If wind blows in the same direction as sound(Fig. 5(b)), the distance from the starting point of vector to asymptotic point (center of shrinking spiral) is nearly equal to that of no wind case(Fig. 5(a)). This means sound amplitudes are nearly equal in both cases. If wind blows against sound(Fig. 5(c)), the distance becomes small and attenuation becomes large. The discussions above stand if there is a screen as shown in Fig. 6, but are not exactly correct when there is ground surface as shown in Fig. 4. Fig. 6 should be considered as the approximation of Fig. 4. In the computation, multiple reference spheres are considered(Fig. 8), which are the approximation of the case in which there is ground surface as shown with a broken line in the figure. The distance between the reference spheres should be so small that only the phase of elementary waves changes and the amplitude does not. Secondary waves from Q to P is given by eq. (4). The column vector composed by the waves at each element of different height on (i+1)-th reference sphere is calculated according to eqs. (5)-(9) from the similar vector on i-th sphere and the phase shift caused by wind. These are the fundamental equations for calculating wind effects. Several computation results are shown in Figs. 9-12. In most cases, the wave elements on reference spheres are considered from 0 to 40 m height at 5 cm intervals, and the distance from one sphere to the next is 20 m. Sound source height is 1. 4m, and attenuations at various receiver height are plotted. It is observed that when wind blows against sound, large attenuation occurs at low receiver position and long distance. At heigh receiver position, attenuations are almost equal to that of geometrical spreading(inverse square law). As sound wave length becomes shorter, attenuation at low position becomes larger. Even there is no wind, attenuation occurs at low receiver position. This is the effect of diffration by multiple screens, and approximates the effect of fully sound-absorbing ground. This paper concerns only one aspect of sound propagation outdoors. Many other factors should be considered in practical problems.
- 社団法人日本音響学会の論文
- 1978-05-01