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_<pe>| 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_<pe>| 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.
It is well known that the noise pollution in our cities is chiefly caused by road traffic noise and the polluted area increases rapidly with the development of a city. Generally speaking, in the problem of noise control, a systematic prediction of the statistics of noise level before the establishment of a new road is, of course, more important than the case-by-case countermeasures applied after the completion of new roads. In this paper, a new attempt to solve the above prediction problem in terms of the level probability disribution from which all information concerning the lower and higher order moments of noise level can be derived is theoretically considered in connection with the internal structure of traffic noise (e. g. , the distance from an observation point, environmental noise level distribution, and, as controllable quantities, the average number of vehicles flowing on the new road, the mean velocity, of the vehicles, the ratio of the number of large-type vehicles to that of small-type vehicles, their acoustic power levels, etc. ). More concretely, for the purpose of predicting the effect of vehicle noise on the level probability distribution, an explicit expression for the probability density function of urban noise fluctuation after the completion of a new road is derived in the general form of a nonorthogonal expansion series including the effect of the enviromental noise level before the establishment of the road as the first term (cf. Eq. (11)). The effect of internal structure on traffic noise is reflected successively by each expansion coefficient (cf. Eq. (24)). The validity of our prediction theory is also supported experimentally by a digital simulation technique.
This paper deals with the optical transmission characteristics and dielectric effect of nematic liquid crystal (MBBA) films when a vibratory shear wave is applied. The experimental arrangement for the measurements is illustrated in Fig. 1. The relative change of the transmitted light intensity as a function of the shear wave displacement is shwon in Fig. 2-4, for the case when (A) H_e-N_e laser is used as the light source with a cross nicol system, (B) unpolarized light from a H_e-N_e laser, (C) incandescent light with a cross nicol system and (D) unpolarized incandescent light. It is found in these optical characteristics that there exists a threshold displacement for vibratory excitation above which molecular orientation occurs. The effect is similar to that observed for the application of magnetic or electric fields. These values are almost constant, independent of the film thickness (66μm, 105μm and 153μm). A theory is developed based on the continuum elasticity theory, with which the experimental results can be explained with respect to this threshold-thickness relation. The theory also states that f・x should be constant, where f and x are the vibratory frequency and displacement, respectively. However, this relation did not hold for the experimental results, which is probably due to the fact that the liquid crystal is not simply of a linearly elastic fluid as assumed in the theory. For a further increase in the vibratory displacement, a complex transmission characteristic due to a retardation effect is observed. A parallel domain structure appears in the liquid crystal film, in which its space frequency increases with displacement (Fig. 9(a) and (b)). Then celluar motion is observed and finally DSM is acheived (Fig. 9(c) and (d)). Once DSM is generated, the transmitted optical intensity decreases linearly with the logarithm of the displacement. The intensity decay rate is rather low for the sample of 153μm thickness (Fig. 10(a)), while the intensity declines sharply for the other cases. In this range, vortices often appear in the liquid crystal film (Fig. 10(d)), which produce an abnormal effect on the transmitted light intensity. For comparision, the optical effect by the application of AC and DC electric fields is also examined (Figs. 5-7). The optical effect of the vibration is found to be similar to the latter case, though the domain structure as well as the DSM are not exactly the same (Fig. 11). It is also found that the dielectric constant and the tan δ of the liquid crystal change when a vibration is applied. Their relative change as a function of the vibratory displacement is shown in Fig. 8. The dielectric constant increases with displacement above the threshold, while tan δ decreases. This can be explained well by the process of rotation of the molecular orientation, together with the negative dielectric anisotropy of MBBA. The continuing increase of the dielectric constant is also observed over the range of the domain structure, until it is saturated with the generation of DSM, while tan δ has a minimum value.