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.

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A Piezoelectric type receiver is a useful device to be placed on the ground surface for reception of impulsive echo signals from bodies buried in the underground, because it has a capability of receiving signals of wide frequency band, and is simple and small-sized in structure substantially. In this paper are described a means to get close contact of the receiver attachment with the ground surface, together with theoretical and experimental analyses about reception characteristics of the receiver. The receiver is composed of two PZT disks cemented on an aluminum attachment and an aluminum disk cemented on the PZT disks. In order to find a means to get close contact of the receiver attachment with the ground surface, experiments were performed by an apparatus shown in Fig. 2 with several receiver attachments shown in Fig. 1. The results are shown in Fig. 3 and Fig. 4, from which it was concluded that the contact surface of the receiver attachment with sharp V-grooves as shown in No. 4 of Fig. 1 is most suitable and insertion of grease-sand mixture (weight ratio 1 : 3) between the attachment surface and the ground (sand) produces a close contact. Equation (6) expresses the relation between the sound pressure p of the incident plane wave and the output voltage E_o of the receiver placed on the ground surface. Fig. 6 shows the frequency characteristics of the receiver sensitivity calculated by Eq. (6). Fig. 6 indicated that the receiver sensitivity in the low frequency range increases proportional to frequency and the maximum sensitivity is obtained at Ω=1, and the receiver sensitivity decreases a little even in the higher frequency range in case of low mechanical Q. Eq. (11) and Eq. (12) express the radiation resistance and the stiffness of the receiver respectively. Fig. 7 gives the relation between mass M_T and diameter 2a of the receiver as functions of wavelength λ_po and mechanical Q calculated by Eq. (16), using ρ_s=1. 45 g/cm^3 and B=0. 1486. M_T and 2a can be determined from this chart by giving λ_po and Q. Eq. (17) expresses the output of the receiver when the waveform of the incident sound is impulsive. Measurements of the mechanical resonance frequency and the mechanical Q of the receiver placed on the ground surface were carried out in order to justify the theoretical expressions. Fig. (8) and Fig. (9) show the sound source, the receiver and the measuring apparatus used in the measurement. For the sound source, an electromagnetic induction type sound source was used. Resonance frequency in the transmitting electrical circuit was changed by three steps of 5 kHz, 1. 82 kHz and 0. 87 kHz. Mass of the receiver was changed by five steps of 260g, 420g, 600g, 1200, g and 2460g by rescrewing the brass rod with various weights in the main body of the receiver. in Fig. 10, the waveform of the receiver output in case of 0. 87 kHz driving current frequency and 1200g mass of receiver is shown. Resonance frequencies were obtained from periods of the received sound waveforms except for the first half cycle. in Fig. 11, the results are compared with the theoretical values of the mechanical resonance frequencies calculated by Eq. (13) using c_p=300 m/s (measured value). Mechanical Q's were obtained from decay curves of the envelope of the received sound waveforms. In Fig. 12, the results are compared with the theoretical values calculated by Eq. (14). From the fact that the measured values agree with the calculated ones with reasonable accuracy, it is confirmed that the radiation impedance of the receiver is expressed by Eq. (11) and Eq. (12).

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The resonator with directional converter was analyzed already. However, the converter is usually used as an element in a system of a vibrational transformation rather than a separate devics ; so that, it will be very convenient for understand a vibrational system as a whole, if the converter can be represented by an electrical equivalent circuit. From this point of view, the authors tried to analyze a L-L-type converter by its electrical equivalent circuit. The converter was divided in two principal parts, each part of four bars and one connecting part. Each part of bars was expressed by a four-terminal network of a distributed constant circuit and a connecting part was expressed by a four-terminal network of a concentrated or lumped constant circuit. Then the converter was indicated by four terminal network (see Fig. 2〜5), as vibrational modes of the converter in resonances were symmetric with respect to two axes. Thus, the frequency equation (35) and the equation (37) of the vibrational velocity ratio at each free end of the converter were derived. From this study, it was found, by referring to the other report, that these two equations were applicable to the converter with the connecting part which is small enough as compared with a wavelength of two axial directions, and were able to describe well its vibrational characteristics also.

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This paper describes a new method of feature extraction from speech spectra based on multi-category linear discriminant function. Five Japanese vowels pronounced by 24 male speakers and 26 female speakers were analyzed by a filter bank (Fig. 1). Then four components were extracted from the output of the filter bank by this method and a vowel feature space was constructed by these four components (Fig. 3). 96% of these vowels were identified correctly using only two of the four components and 98. 6% using all the four components. It was shown that this method gives a better result than principal-component analysis under the same condition (Figs. 4 and 5). The coefficients calculated from the sample vowels were also applicable to new sample vowels (Figs. 6 and 7). Furthermore, the first and the second components were found to be highly correlated with the first and the second formant frequencies, respectively (Figs. 8~11). The trajectories of combined vowels /ie/, /ia/, /io/ and /iu/ in the first and the second component plane were similar to their trajectories in the F_1 - F_2 diagram (Fig. 12). From these experimental results, this method is expected to be useful for real time feature extraction from speech signals.

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The ultrasonic velocities of the mixtures of benzyl alcohol and methanol, ethanol, n-propanol and n-butanol were measured with a high pressure type ultrasonic interferometer at a frequency 4 MHz. The measuring pressure was up to 300 atm and the measuring temperature was 30℃. The ultrasonic velocities of these alcohol mixtures increased with the increase of pressure parabolically and decreased with the temperature rise linearly. As an illustrating example of experimental results, the pressure and temperature dependence of the ultrasonic velocities in these mixtures were shown in Fig. 1 and 2 for the mixtures of benzyl alcohol and n-propanol. From these results, the non-linearity parameter, B/A, were determined. These values were summerized in table 5-8. As is seen in these tables, the non-linearity parameters were almost constant in spite of the fact that the pressure coefficients of ultrasonic velocities varied lineary with the mole fraction in each of the alcohol mixtures.

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