A theoretical and experimental study of the influence of air flow on the attenuation characteristics of a single expansion chamber filter is presented. The acoustic energy dissipation caused by air flow at the open end is counted for the equivalent resistance ρ_0cM which derived from Eqs. (1)-(4), where ρ_0c is the characteristic impedance of air and M is the Mach number of air flow. From Eqs. (6)-(8) and Eqs. (14)-(16), one gets the equations for the particle velocity at each area change in a tube with air flow, which was described by Eq. (9) and Eq. (17), and the effective cross-sections ratios σ_M and σ_(M') are obtained. Assuming that the area changes of a single expansion chamber filter can be expressed by these effective cross-section ratios, the attenuation characteristics of the filter with air flow for a reflection-free source and a constant-pressure source can be given by Eq. (28) and Eq. (31) respectively. The theoretical values of the sound attenuation for a constant pressure source are compared with the measured values over a range of mean-flow velocity U≤40m/sec. The results are shown in Fig. 7.

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In order to design n artificial mouth measured for loudness, the knowledge of a property of diffraction coefficient of variously obstacles combined with the human mouth and with a spherical sound source is important. Therefore, we measured diffraction coefficients of various obstacles combined with the human mouth and with the spherical sound source, a detailed comparison of the diffraction coefficients of both methods is made. The diffraction coefficient of the obstacle as shown in Fig. 1 is represented as Eq. (4), where D_0 denotes the diffraction coefficient of the obstacle which is replaced with a rigid body, Z_L denotes input impedance viewed from the surface of the obstacle, and Z_r denotes radiation impedance of the obstacle combined with the sound source. The obstacle used in experiments to determine whether Eq. (4) is good or not was a telephone transmitter of the Japanese commercial type. The measured values of Z_r combined with the human mouth and the spherical sound source are shown in Fig. 3 and an equivalent circuit of transmitter is shown in Fig. 4. As numerical results of 20 log_(10)|Z_L/(Z_L+Z_r)|, which are shown in Fig. 5 by the solid line and the dotted line, agree with the experimental results of D/D_0 as shown in Fig. 5 by the experimental points, it becomes evident that Eq. (4) is good. Diffraction coefficients of variously shaped rigid obstacles placed in front of the human mouth at a distance of 2 cm are shown in Figs. 6〜10 by the marks (・) represented as mean values, and diffraction coefficients of the same obstacles placed in front of the spherical sound source (20 cm in diameter with a vibrating part 5 cm in diameter) at a distance of 2 cm are shown in Figs. 6〜10 by the solid line. On the basis of these experiments, it seems that diffraction coefficient depends on the front shape of obstacle, since it is large for a flat shaped obstacle and small for a spherical shaped obstacle. Although the diffraction coefficients are very different according to the shape of the obstacle, the difference between diffraction coefficients combined with the human mouth and with the spherical sound source is obtained with better accuracy than with 2 dB. (Fig. 11)Diffraction coefficient D_0 of the telephone transmitter of the Japanese commercial type is shown in Fig. 12. The difference between diffraction coefficient combined with the human mouth and with the spherical sound source as shown in Fig. 11 by the marks(□) agrees with the average value of the previous variously shaped obstacles. When the distance between the sound source and the obstacle is varied, and the obstacle is inclined, the diffraction coefficients D_0 of a circular disc and the telephone transmitter are shown in Figs. 13〜16. When the distance between the sound source and the obstacle is 2 cm, the diffraction coefficient D_0 below 2 kHz does not change of the obstacle is inclined at an angle of 45゜. On the basis of these results, it becomes evident that the system of the human mouth and the telephone transmitter is approximated by the system of the spherical sound source and the circular disk.

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The ever-increasing use of electromechanical resonators vibrating in flexural modes of tuning forks, free-free bars and cantilevers in various fields of communication and control calls for another look into the mounting techniques, which can yield a more compact overall size without impairing the stability and Q of the vibrators. The mounting technique presented in this paper utilizes the supporting flexural vibrators which are inserted between the main vibrator and the base. The length of the supporting vibrator is chosen to be a quarter or a half wavelength so that the free or fixed boundary condition can be realized at the junction between a supporting vibrator and the main vibrator. Man features of this technique are :(1) The coupling between a supporting vibrator and the base can be kept to a minimum. This is because the thickness of the supporting vibrator is so thin that a nearly perfect fixed condition is realized at the junction between the supporting vibrator and the base. This improves Q and suppresses variations in resonance frequency due to environmental changes. (2) The length of the supporting vibrators is proportional to its thickness and can therefore be made very short. This makes the miniaturization of the overall size possible. (3) Supporting points are not restricted to the nodal area of the main vibrator. Even support at the antinodes is possible. This makes the design of anti-shock mountings easier. Also such vibrators as tuning forks and multiple mode resonators which have no definite nodes can be easily mounted. Characteristics of a typical mounting structure, in which a main bar vibrator is supported at one end by a collinear cantilever vibrator, are analyzed, based on the flexural vibration theory of a composite bar. Spectra of resonance frequency were calculated as functions of the length of the supporting vibrator and compared favorably with experimental values obtained for the following two vibrators. One vibrator was so designed that the main vibrator was able to vibrate in a free-free flexural mode and hence the length of the supporting vibrator was able to be a quarter wavelength. The calculation of displacement shows that a proper choice of the supporting length yields a displacement pattern closely matching the pattern of a perfect free-free bar. Another vibrator was designed so that the main vibrator was able to vibrate in a fixed-free flexural mode and hence the supporting length was able to be a half wavelength. Both theory and experiment show that only the second or higher fixed-free mode can be realized but not the first mode. Hence the quarter wavelength mounting is preferable to the half wavelength mounting from the view point of miniaturization. The determination of the supporting length based on the matching of displacement requires an interactive calculation. A straight forward determination, however, becomes possible if appropriate boundary conditions are assumed at the junction between the main vibrator and the supporting vibrator. Experiments using various vibrators show that the assumption of the sliding end (where both tangent and shearing stress are zero) gives better results than the assumption of the free end (where both moment and shearing stress are zero), which has been used in the mounting of high frequency quartz vibrators. The overall mounting characteristics of a complete vibrator were evaluated by the change of resonance frequency before and after the clamping of the base by a heavy vise. Quarter wavelength of a free-free bar, a tuning fork and a multiple mode vibrator with a rectangular cross section and half wavelength mounting of a cantilever vibrator were tested and yielded good results. A complete filter utilizing the multiple mode vibrator was also made, to show the compactness obtained by the present mounting technique.

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The ultrasonic velocities of methyl, ethyl, n-propyl, and n-butyl acetate were measured with high-pressure type ultrasonic interferometer at a frequency of 4 MHz. The measured pressure was up to 300 atm. , and the temperature range was from 5℃ to 35℃. The ultrasonic velocities of these esters increased with the increase of pressure parabolically, as shown in Fig. 3 to Fig. 5 and decreased with the temperature rise linearly as shown in Fig. 6. From these results, the non-linearity parameters, B/A, were determined. These values were summarized in Table 1. As in seen in Table 1, nonlinearity parameters were almost completely due to the pressure dependence of sound velocity and independent of the temperature. On the basis of the oscillator-model of liquid, the following equation was derived;1/C(∂C/∂P)/β_T=(n+m+3)/6From this equation, the indexes of Mie's potential, n+m, were determined from the data of the pressure dependence of the sound velocity and iso-thermal compressibility. These values were summarized in Table 3, which were in good agreement with the data obtained by Moelwyn-Hughes by the static method.

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