An automobile compartment is considered as an irregularly shaped acoustic field enclosed by body panels. The purpose of this paper is to report on a numerical investigation of an acoustic field of general shape, while it is impossible to get the exact solution of normal frequencies or sound pressure distributions of such a field. The calculation method used in this paper is based on the usual finite difference method, but a special consideration is paid for an approximation of the boundary-condition equation (Eq. 5) in order to improve the accuracy of calculations. Eq. 2 or Eq. 3 is wave equation and it is approximated by the finite difference equation given by Eq. 4. A set of simultaneous equations on the sound pressure of interior grid points (Eq. 12 or Eq. 13) is generated by using the suitable relation described in Eq. 7〜Eq. 11 for the approximation of the boundary-condition equation in each boundary illustrated in Fig. 2, where, the quadratic in stead of linear distribution of the sound pressure around the boundary is assumed (Eq. 6). In this way much error can by avoided without involving a longer computation time and a larger computor memory. In case all the boundaries are rigid (V_n=0 in Eq. 5), the set of equations is homogeneous and it is reduced to the eigen value problem as expressed in Eq. 12. The eigen values (normal frequencies) and the eigen vectors (sound pressure modes) are obtained from this equation. The calculated normal frequencies of the lowest four modes for a rectangularly shaped room converge on the exact solution as the grid size vanishes (Table 1). For a trapezoidal shape model, both results obtained with coarse and fine grids quite precisely agree with experimental values as shown in Fig. 3 (normal frequencies) and Fig. 4 and Fig. 5 (sound pressure modes). When some parts of the boundary are given arbitrary vibration (V_n), forced vibration problem of the acoustic field must be studied. The sound pressure gradient which is equivalent to the vibration velocity of the boundary panel forms constant terms of Eq. 13. The sound pressure at each interior grid point is evaluated by solving this equation. The response of forced vibration (Fig. 7) gives the `transfer acoustic impedance density' that is the sound pressure at an arbitrary point in the field radiated from a panel of a unit area vibrating with unit velocity. This result shows that a vibration of the panel which faces an anti-nodal part of sound pressure modes has a higher sensitivity for the interior sound pressure than the one which faces a nodal part. Fig. 9 shows the calculated sound pressure of interior points for various vibration modes of boundary panels. The interior sound pressure can be predicted as the resultant vector of the sound pressure which is radiated from whole boundary panels. This indicates that the vibration prevention of boundary panels does not always reduce the interior sound pressure. The present paper lays emphasis on the calculation method and includes only a simple example. But the results for more complex shapes which simulate automobile compartments verify the method that is mentioned. The effective consideration for the vibration of body panels is also expected for the purpose of reducing the interior noise of an automobile. These are to be discussed at another opportunity.

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Here, two experiments were carried out on the attack transient of pure tones, with special regard to the differences in tone quality of natural musical instruments and an electronic musical instrument. In this paper, we refer to the results of the second experiment. The details of the first experiment are mentioned in a separate paper. In the first section in order to examine the auditory characteristics of 34 clusters, classified mathematically in part 1, a sound synthesizer was constructed, which can generate various attack forms at will so far as the quantized time and intensity are concerned. By selecting several representative patterns from each cluster, experiments were carried out to examine, (1) whether the patterns classified into different clusters are auditorily different or not, and (2) whether the patterns classified into the same cluster are judged to be very similar or not. The results, as shown in Fig. 2 and Fig. 3, indicate that (1) the 34 clusters may be re-classified into eight groups, and (2) most of the patterns within the same cluster are judged to be of the same quality. Second, although the experiment in part two is carried out with sound synthesizers, future simulation research should be made by means of a digital computer. In order to synthesize these attack transient patterns with digital computers, formulation has been attempted in terms of a cascaded exponential function and a step function of eight groups of patterns. The formulae are shown in Table 2. As pointed out at the outset, the attack pattern of overtones for natural musical instruments can vary independently. In the design of tone quality of electronic musical instruments, one must take into consideration such phenomena. Digital computers will show a greater degree of freedom in this respect.

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Interuaral intensity or time difference carries the information on the direction of a sound source. But if there is a preceding sound leading the signal (the following sound) this information is masked by the preceding sound and the detection threshold of the following one with interaural intensity difference varies from one with interaural time difference. This fact shows that the effect of the preceding sound on the following one depends on whether the information of direction is carried by interaural intensity difference or interaural time difference. This article describes the effects of the preceding sound on localization of the following one and obtains the time-intensity trading ratio as a function of the intensity of the preceding sound. The results obtained are as follows. 1) The minimum detectable changes of the interaural time difference for the higher frequency tone burst are more influenced by the preceding sound than for the lower frequency tone, and the minimum detectable changes of the interaural intensity difference for the lower frequency tone are a bit more influenced by the preceding sound than for the higher frequency tone (see Fig. 2). 2) The minimum detectable changes of interaural intensity difference for the longer duration are smaller than those for the shorter one. On the other hand, the minimum detectable changes of the interaural time difference for the longer duration are greater than those for the shorter duration (see Fig. 3). 3) The minimum detectable changes of interaural intensity difference are little influenced by the time interval between the preceding sound and the following one, while the minimum detectable changes of interaural time difference are much influenced, and, further, it increases along with an increase of the intensity of the preceding sound (see Fig. 4). 4) The time-intensity trading ratio is more influenced by the preceding sound for the time interval of 5 msec between the preceding sound and following than 25 msec, that is, the trading ratio abruptly increases, in the former situation, along with an increase of the intensity of the preceding sound (see Fig. 6). 5) When the time interval between the preceding sound and the following is 5 msec and the intensity level of the preceding sound is 0 dB relative to that of the following, the trading ratio changes into negative (see Fig. 6). 6) An increase of the trading ratio accompanied by an increase of the intensity of the preceding sound is greater for 5 msec duration than for 20 msec (Fig. 6) These results show that the information of interaural time difference is more easily masked by the preceding sound than one of interaural intensity difference, so that the lateralization is more affected by interaural intensity difference than by interaural time difference when the preceding sound is present. The results may be interpreted as follows. 1) Since the sound with interaural time difference has interaural difference at their onset, while the sound with interaural intensity difference has its difference at the steady part, the information of interaural time difference is more easily masked than one of interaural intensity difference. 2) If the time-intensity trading is caused by neural latency, the slope of the curve of the latency vs. sensation level (see Fig. 10) is regarded as the trading ratio. When the preceding sound is present, the threshold of the following one is raised by the forward masking, and the effective level of the sound decreases. Thus the trading ratio increases according to the curve. The results calculated from the latency curve are shown in Fig. 11, which are consistent with the results of the experiment 2 (Fig 6).

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