The Sound Reflection from a Rigid Cricular Plate in Oblique Incidene

Abstract

A calulation method for the amplitude of reflecting sound wave from a circular disc of finite size which has oblique incidence is derived in this parer. This method is expressed in the term of the "extended reflecting power". The "extended reflecting power" is the ratio of the sound pressure of the reflected wave from a circular disc at the position of the receiving point to the sound pressure of the incident wave at the distane X+Y from the sound source. X and Y are the distance from the center of the disc to the sound source and that to the receiving point respectively. Sound reflection is calculated by Fresnel-Kirchhoff difraction formulas. It is assumed that the wave length λ is fully smaller than the radius of the disc R and the distances X and Y are sufficientely larger than the radius. Under these assumption, x and y, which are the distance from the element of a surface area ds of the disk to the sound source and that to the receiving point, are given by Eqs. (5) and (6). The relation of incident wave is given by Eq. (7). From above relations, the absolute value of the "extended reflecting power"|R_&ltpe&gt| is given by Eq. (8). This relation is simplified to Eqs. (10), (11), (12) and (13). Some experiments were executed so as to verify the validity of these formula. These were performed in the air at the frequency of 39. 90 kHz. Fig. 3 shows the arrangement of the apparaturs in the experiment. Two piezoelectric transducers were put toward the circular disc which was made of hard plastics. The pulse width of the sound wave from the transmitter was 1. 38 ms. The amplitude of the reflected pulse was measured on the screen of C. R. O. . Figs. (5) and (6) show examples of the results of these experiments when the angle of incidence is equal to that of reflection. Fig. (7) shows the relations between X and Y when the reflectivity is minimum. The results of these experiments are in quantatively reasonable agreement with the numerical results of Eq. (10). when the angle of incidence is comparatively small. Fig. (8) shows experimental and theoretical values of |R_&ltpe&gt| when the sound source and receiver were put on the same point as shown in Fig. 3(b). Fig. 9 shows the experimental and numerical results when the sound source was put on the axis of the circular disc as shown in Fig. 3(c). Fig. 10 shows the results of the directivity of the extended reflecting power of small discs. In these experiments, the results quantatively agree with the theory when X and Y were sufficientely large. From the results of above experiments, it is found that the calculation method for the reflection of sound wave from a circular disc of finite size is useful when the angles of incidence and reflection are comparatively small and the distances X and Y are sufficientely larger than the radius of disc.