Acoustic cavity has been studied by numerous investigators from different points of view. As is well known, a cavity behaves as a typical lumped capacitance element, provided that the wavelength of sound is sufficiently large compared with the dimension of the cavity and that viscosity loss can be neglected. This simple characteristic of cavity is widely used to the design of acoustic devices based on circuit theory. On the other hand, detailed investigations based on wave theory show us the complex behavior of cavity depending on wavelength of sound as well as shape and dimension of the cavity. In this paper wave theory is applied to a cylindrical cavity which is obtained by rigid or another suitable termination of an acoustic transformer element with a simple plane discontinuity of circular cross section (See Figs. 1 and 6), and the sound field and input impedance of the cavity are determined. Based on the exact theory, a systematic approach to plane-piston approximation and plane-wave approximation is made in order to clarify the differences as well as the limitation of each of the approximate methods. Comparison of input impedances obtained from these approximate methods and exact theory is given in Figs. 2 and 7. Next, the pressure distribution along the axis of the cavity is measured by using the standing wave method, of which several examples are shown in Figs. 8 and 9. In addition to the measured values, the calculated values are also plotted in the above figures and they are in good agreement with each other. Moreover, the equivalent circuit representation of the cylindrical cavity is compared with one corresponding to the acoustic transformer and the relationship between them is discussed.
As part of basic research on acoustic transmission systems and their elements, wave theory is applied to acoustic transmission ducts with circular cross section whose radius varies in a stepwise manner. In the present paper we try to deal with three typical types of stepped acoustic transmission ducts with two plane discontinuities as shown in Figs. 1, 4 and 7. These are rather simple acoustic transmission elements, but their characteristics are more complicated than those of acoustic transformers and cavities treated in previous papers. They are widely used in the design of acoustic devices as an acoustic filter-element. They are also expected to play an important role in the analysis of more complicated transmission systems. The purpose of this paper is to investigate the sound field in the stepped ducts and to clarify the transmission characteristics of these elements to the plane incident wave, P_oexp(iωt-ikz). Corresponding to the stepped ducts shown in Figs. 1, 4 and 7, their pressure distributions along the axis are plotted in Figs. 2, 5 and 8, respectively. Relevant acoustic characteristics of the ducts such as transmission and reflection coefficients, transmitted and reflected powers are also given in Figs. 3, 6 and 9. By examining these figures we may be able to understand the effects of higher order modes on a plane wave propagating in the stepped ducts. These higher order modes are excited at the plane discontinuities. At high frequency range they have a great influence upon the sound field as well as acoustic coupling between discontinuities. Moreover We may be able to compare and discuss the acoustic characteristics of each of the stepped ducts by referring to the above figures.
Acoustically transparent visual structure walls such as slat- and grid-walls have been widely used in the ceilings of large studios and halls, but few quantitative data for the acoustical designing of visual walls have been available as yet and the method of calculating, reverberation time in the room provided with visual walls has not been established yet. In order to make these points clear, reflection and transmission characteristics of slat- and grid-walls were studied by means of scale models. Data obtained from this study were used for discussing the method of designing the room provided with visual structure walls. A finite square plate with an area of 20×20cm^2 was selected as a test-piece in this study. A square aperture of the same area as the test-piece was made in a partition in an anechoic room to receive the test-piece in it. The transmitted or reflected sound pressure was measured as functions of the angle of transmission, that of reflection and frequency. Characteristics of the test-piece of the infinite area were examined on the basis of the diffraction theory, from the results of which characteristics of walls of an infinite area were derived. Acoustic transmission through and acoustic reflection on slat-walls relate to the ratio of the slat period L to the wavelength λ of an incident sound. When the ratio L/λ is smaller than 0. 8, the greater part of an incident sound transmits through slat walls. On the contrary, when the ratio is larger than 1. 6, an incident sound reflects in proportion to the surface ratio of the slat. The reflection on grid walls mainly relates to the depth of the grid, while the reflection coefficient of grid walls more than 10cm in grid width and less than 40cm in grid depth is 0. 1 at most in the frequency range below 4 kHz. From the results of study made by means of a model room of the method of calculating reverberation time in the room provided with visal structure, it has been concluded that (1) in the frequency range in which the reflection coefficient of structure walls is small, reverberation time should be calculated with respect to the whole space of the room including the rear part of the structure with the absorptivity of the visual walls shown in Fig. 12 considered to be additional absorptivity, and (2) in the frequency range in which the reflection coefficient is large, reverberation time should be calculated with the space inside the visual walls considered to be the room capacity on which an acoustic design should be based and with due regard paid to the effective absorptivity of the visual walls.