The dynamic depolarizing-field effect in a long piezoelectric bar under the longitudinal-effect extensional virbration has been investigated. Fundamentals are described in the paragraph 2. The depolarizing field is caused by the space and surface free charges due to the spatial distribution of the polarization associated with sound waves. The present analysis is based on the following four assumptions: The physical property of the bar is axially symmetric and dielectrically isotropic.  The strain S_3 depends only on z (lengthwise direction).  The vibration is excited by alternating true charge on the end electrodes or driven by the alternating stress applied upon the end faces.  The field produced by the charge is approximated by that due to the changed disc or ring. In the paragraph 3, fundamental equations are established to determine the distributions of polarization and strain. The space free charge in the interior and the surface charge on the side face are derived from (3. 6) and (3. 9). Then the depolarizing field is given by (3. 13) or (3. 13'), which leads to an integral equation [A] (3. 15), the 1st fundamental equation. The wave equation brings the 2nd equation [B] (3. 20), and the 3rd one [C] (3. 25) is obtained from the boundary condition at the end faces. In the case of sound propagation along an ifinitely long rod (paragraph 4), simulatneous equations [A] and [B] can be exactly solved for L→∞, and the dispersion relation is given by (4. 11) or (4. 13)〜(4. 15), where an effective compliance s_eff and an effective electromechanical coupling coefficient K are introduced. The problem for the vibration of a finite bar (in paragraph 5) can be approximately solved by replacing K(y) with K_a(y) (eq. (5. 1)), where the parameters are chosen as mentioned in Appendix A. 1. (All of the appendices will be described at the end of the succeeding paper. ) The solutions take the forms of (5. 3) and (5. 4), where k and λ_i's should satify eq. (5. 19) with respect to Λ. The P'_k and P'_i's are given in (5. 22) and (5. 23), respectively. (Details of derivartion are described in A. 2. ) It is assumed that the wave number k(x) defined in eq. (6. 2) is nearly equal to k. Then the dispersion relation is given by (6. 4) or eqs. (6. 5)〜(6. 7) in the same forms as those in the case of an infinitely ong rod. The admittance of vibrator is obtained as shown in (6. 8), where the parameters U etc. implicitly involve χ, k^^^〜^2, k and L. In order to get more simple expressions convenient for use, various quantities are given in the alternative forms by (6. 12), (6, 13) replacing U etc. by u etc. as shown in (6. 11). The admittance is thus expressed by (6. 17). The constants of the vibrator, , k^^^〜^2 and v, are evaluated by (6. 24) as described in 6. 2 using ω_R and ω_A obtained by the resonance-antiresonance method. In the case of small w, the admittance is expressed in the simple form of (6. 25). This expression is characteristic of the admittance for the electromechanical transducer with logitudinal-effect coupling. The antiresonance occurs at a frequency near the half wavelength frequency 1/(2l√ρs_<eff>). The L-dependence of resonant and antiresonant frequencies are shown in Fig. 2. Numerical values of the various parameters Φ's and ψ's in the foregoing formulae are shown in Fig. 3, which serves for the experimantal determination of electoromechanical constants of the bar. The present result improves the Ogawa's result reported early.
The dynamical demagnatizing-field effect in the sound propagation along a piezomagnetic (or biased-magnetostrictivce) rod has been studied. The procedure of the analysis is almost the same as that in the piezoelectric case reported in the preceding paper. In the present case, however, the nature of the driving field differs from that in the piezoelectric case. Therefore the assumption in the previous paper should be replaced by the following. [3'] The vibration is excited with the magnetic field produced by the electric current through a solenoid or driven by the alternating stress on the ends. The demagnetizing-field is given by (2. 5), and the inner and outer driving magnetic fields are given by eq. (2. 7), of which the amplitude h_0 is related to the current I by eq. (2. 9). Fundamental equations are given by [A] (2. 11) and [B] (2. 14). An exact solution is obtained as reported in the preceding paper in case of infinitely long rod. For the vibration of a finite bar, equations [A] and [B] are approximately solved under the condition [C] (4. 1') using the approximation K_a(y). The results are obtained as (4. 2), (4. 3), (4. 10) and (4. 11). The impedance of the vibrator is determined as (5. 6), and is further expressed in the alternative from (5. 7) using (5. 12) and (5. 13). In the case of small w, it is transformed to the simple forms of (5. 21) and (5. 22). It is noticed that the electrical behavior of the present piezomagnatic bar is rather of transverse-effect-type despite of its logitudinal-effect coupling, in contrast to the conculusion obtained for piezoelectric bar in the preceding paper. The resonance occuers at a frequency near the half-wavelength frequency 1/2l√ρs_<eff>, which decreases with increasing length as shown in Fig 1. Numerical values of the parameters are given in Fig. 2 to serve for a practical use in the electromechanical measurement.
One of the typical interference factors which should be taken into account on using loud speaker telephone is the deterioration of speech quality caused by reverberation. To investigate such effects of reverberation, the speech qualities of artifical and real room reverberation were estimated from the viewpoint of preference. In order to simulate the simple phenomenon of reverberation in this experiment, the colorless artifical reverberation equipment proposed by Schroedere was composed with a digital and an analogue computers. Because the reverberation equipment has the simple feedback system comprising three amplifiers and one delay element (Fig. 1), it is easy to change some physical parameters of reverberation. For subjective measurement, preference tests were carried out by the pair comparison of two signals. The one is speech with reverberant and the other is the original speech added with white noise. From these results, the signal to noise ratio at 50% preference point, defined as equi-preference signal to noise ratio, was determind. In order to remove the effect caused by the different delay time of artifical reverberation, the normalization was carried out. The equi-preference signal to noise ratio of speech with artifical reverberation and reverberation speech in real room is shown in Fig. 4. According to the results of these experiments, the quality of reverberant speech can be expressed by a signal straight line in the region of reverberation time T_r shorter than about 250 or 300 msecs. Therefore the relation equi-preference signal to noise ratio with T_r is shown by the equation (2). Under the condition that the impulse response representing reverberation decays exponentially with time, it can be rewritten as the equation (7). The equation (7) is similar to that giving the Definition or Clearness by Mayer, that is such value that the energy in first 50 msec of the impulse response is divided by the total energy. Therefore the preferable signal seems to be the total energy of direct sound and the following sound. On the other hand, it is considered that the energy of sound coming about 40msec after direct sound acts as interfering noise in view of preference for telephone transmission system. In order to cerify this supposition, other preference tests were carried out by the pair comparison of speech followed by echo and noise-added speech. The result shown in Fig. 8 suggest that the echoes coming after about 40 to 50 msec cause the same deterioration of speech quality except the case of single echo. From these consideration, it may be useful, in the viewpoint of preference, to suppress the component of sound energy coming later than about 50 msec for telephone transmission system.
Many papers have reported on the one-dimensional analysis of an ultrasonic solid horn in half-wave resonance. However, there is a considerable difference in behavior between the horn analyzed by the one-dimensional theory and the horn produced practically by the one-dimensional analysis. As many ultrasonic solid horns are axisymmetric, their vibration is analyzed two-dimentionally and axisymmetrically by means of the finite element method. In this paper, an exponential solid horn is treated and its free vibration is analyzed for the following two conditions:(1) When both ends are free;(2) When a concentrated mass is attached at the small end. Then, the horn is composed of an assembly of triangular ring elements, and the shape of horn is defined by two parameters d_1/l and d_2/d_1 (Fig. 1, 2, 3). As a result of this analysis by the finite element method, many important vibrational properties of the horn which cannot be obtained by the one-dimensional analysis are found, and the examples of these properties are discribed in this paper. The precision of the values obtained by this analysis is very reliable in the first mode (Fig. 5). As the value of d_1/l increases, the value of αl decreases and the higher modes are drawn near respectively (Fig. 6). The discrepancy between the first resonant frequency obtained by this analysis and that obtained by the one-dimensional analysis is less than 0. 2 percent for d_1≦0. 2 (Fig. 7). The variation of αl as a function of Poisson's ratio ν is approximately linear (Fig. 8). As any inner displacement of the horn is a vector displacement that consists of the axial component and the radial component, the models of the horn vibration are very complex (Figs. 10, 11). The amplification factor obtained by this analysis is equal to that obtained by the one-dimensional theory for d_1/l≦0. 5 (Fig. 9). Then the inner stress of the horn becomes larger, and the flatness of the large end becomes worse in vibration (Figs. 12, 13). The nodal surface, where the axial displacement is zero, is not a plane but a curved surface, and the radial displacement exists even in the surface nodal points (Figs. 14. 15. 16). For d_1/l>=0. 2, as the value of d_2/d_1 decreases, the effect of the supporting point on αl decreases (Fig. 17). As for the horn with a concentrated mass, its properties obtained by this analysis have a same tendency as those obtained by the one-dimensional analysis (Figs. 18, 19, 20, 21). As mentioned above, the results obtainsed by this analysis can serve as a reference for the designing of an exponential solid horn.