- 一般社団法人 日本音響学会
- 日本音響学会誌 (ISSN:03694232)
- vol.29, no.8, pp.445-450, 1973-08-01 (Released:2017-06-02)
It is important in the acoustical engineering to calculate the amplitude of reflected wave from a target. The calculation method has been developed by J. Saneyoshi, who defined the "sound reflectivity of the target" and derived analytically the approximate formulas of the reflectivity. The reflectivity expresses the ratio of the sound pressure of the reflected wave from the target at the position of the sound source to that of the reflected wave at the same position when the target is replaced by an ideally reflecting infinite normal plane. This formula for a circular plate is given by Eq. (10), which is fairly simple and practical. But as shown in Figs. 7 and 8, the discrepancy increases between the results of its numerical calculations and the actual behavior of the reflected wave when the value of the abscissa R/√λX is increased greatly or the distance between the transducers and a target becomes small in comparison with the size of a target. In this paper, the accurate solution for the reflectivity of the rigid targets of simple shape, such as circular plate and square plate, were derived which is applicable to the above case. As shown in Fig. 1, the velocity of the air particles on the target which is located at a distance r from the sound source is given by Eq. (2); φ_i is the velocity potential of the incident wave and k is the wave length constant. The reflected wave can be considered to be equal to the radiated wave from the target which is vibrating at the velocity of -V_N without incident wave. So, the absolute value of the reflectivity is given by Eqs. (12) and (13). Assuming that the shape of the target is circular, the equations are simplified in the form of Eq. (14). This equation becomes Saneyoshi's relation when √X/λ is increased up to infinity. The numerieal result of these equations are shown in Figs. 2 and 3. Some experiments were executed so as to verify the validity of above theories. These were performed in the air at the frequency of 39. 90 kHz. Fig. 4 shows the arrangement of the apparatus in the experiments. Two piezoelectric transducers were put on the axis of the circular plates were 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 the C. R. O. . Figs. 5 and 6 show examples of the results of these experiments. Figs. 7, 8 and 9 show experimental and precise theoretical values of R/√λX divided by the approximate values obtained from Saneyoshi's equation when the reflectivity is minimum. The results of the experiments were in qualitatively reasonable agreement with the numerical results of this precise method.