A theoretical study is made of the corrections for coupler calibration of laboratory standard microphones. In the analysis, the effect of wave motion in a coupler is discussed, taking into consideration the interaction between the microphone diaphragm and the medium. A new method of solving the wave equations, called the infinite-matrix method, is presented in this paper. A coupler is divided into several right circular cylinders and two diaphragms. Each part can easily be solved in general form as an expansion into orthogonal functions. After arranging these solutions in the form of matrix equations with unknown variables, we obtain a system of simultaneous matrix equations by connecting the solutions together. Exact solutions of the wave motion correcting as well as the transmission characteristics for both type 20 cc and 3cc couplers are presented. It is also confirmed that numerical results for the case of the transmission characteristics of the 20cc coupler are rapidly convergent.

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In this paper a number of small size transducersare mounted on a hemisphere so as to obtain a desireddirectivity. The actual directivity Parameter is compared with the desired one at a finite number of points, the best approximation is obtained by minimizing themaximum of the difference. The necessary conditionfor a distribution to give the minimum is formulated, and an iterative algorithm is presented which hopefully converges to a local minimum. All illustrativeexample is given to demonstrate the effectiveness ofthis approach.

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This paper presents the experimental results of vertical vibration tests on small bodies resting on the surface of foundations, and investigates the spring and damping effects of the foundations comparing the experimental results with the approximate theoretical expressions.First, an approximation method of analyzing a soil-body system of vertical direction as a lumped-parameter system consisting of a mass, a spring and a dashpot is described for the cases of both a rigid base and a uniform contact pressure distribution using the Ground Compliance given by Tajimi.Next, the experimental method and the results are presented. The experiments were conducted on two foundations made of Kanto loam sand. The experimental results and their comparison with the approximate expressions are summarized as follows. For the case of Kanto loam foundation, the spring constant and the damping coefficient depend on the average contact pressure and increase as the contact pressure increases (Figs.7 and 11). The spring constant is proportional to the radius of the contact area, and the damping coefficient to the contact area for given value of the contact pressure (Figs.6 and 10). For small values of contact pressure, the measured spring constant is nearly identical to the static spring constant assuming a uniform contact pressure distribution and as the contact pressure is increase the measured value approaches the static spring constant assuming a rigid base contact pressure distribution(Fig.6). The measured value of the dimensionless natural frequency is nearly identical to the value calculated from the approximate expression assuming a uniform contact pressure distribution (Fig.8). The spring team is a function of the frequency and decreases as the frequency increase (Fig.9). Though the measured value of the damping ratio is larger than the calculated value its tendency seems to agree with the approximate expression (Fig.12). The viscosity of the soil seems to have a damping effect on the vibration of a body, though this effect is small compared with radiation damping. For the case of the sand foundation, the effect of contact pressure is considerably large compared with that for the Kanto loam foundation (Figs.14 and 16). This phenomenon is explained as follows: the rigidity of the sand foundation increase locally when a body is set on the surface of the foundation. Because of this inhomogeneity of the sand foundation, sufficient care needs to be taken when a theoretical result assuming the homogeneity of an elastic medium is applied for a sand foundation. However, the size-effect of the contact area on the spring constant and the damping coefficient agree qualitatively with the approximate expressions (Figs. 13 and 15). The dimensionless natural frequency and the damping ratio of the system seem to vary approximately as the -0.4 power of the mass ratio (Figs. 17 and 18).

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Several experiments dealing with temporal summation characteristics in auditory systems were carried by means of jittered pulse trains, and the results are as follows:(1)The audible thresholds of the pulse trains were determined as a function of the pulse density. The results, as shown in Fig. 3, indicate that for repetition rates lower than 10pps there is little change in threshold, and that for the higher rates the threshold becomes lower with increasing repetition rate. The slopes of the threshold curves increase to -3dB/oct. for repetitions rate in the range of 125-250 pps. this characteristic is attributable to temporal integrations in the auditory system. Furthermore, this phenomenon was observed at at about 2 kpps, so it should be considered that there is a temporal summation function in the low stage of the auditory system. The time constant of integration, estimated from these data, is about 30 msec. (2)A similar phenomenon based on temporal summation was observed for the loudness of jittered pulse trains. That is, a pulse train with a higher pulse repetition rate is louder than one with a lower rate. Although this phenomenon is distinct for weak stimuli, it gradually disappears as the stimulating sound becomes more intense(Fig. 5). The mechanism causing these phenomenon is discussed by means of a firing model of the neuron bahased on neurophysilogical evidence and good agreement is obtained. (3)Related to the temporal loudness summation, the effect of loudness on the discrimination on duration was examined. The results are that the duration of sound is perceived based on loudness for durations shorter than 50 msec. but for longer durations no influence of loudness on the perception of durations was observed (Fig. 10, 11). This result was comformed by means of a sound with interaural time difference and light stimuli. That is, in order that the information about the loudness be excluded from the stimuli, interaural time differences and time difference of lighting were used as stimuli and both discriminations were determined. The results that discriminations becomes constant at about 10 msec. for time differences shorter than 50 msec. (Fig. 12, 13). By contract, the discrimination of duration becomes less with the decrease of duration(Fig. 11). these results show that the duration of sound is perceived through integration circuits with a time constant of about 30 msec.

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