Geometrical acoustics shows that the directivity pattern of sound radiation through an operating in a diffuse sound room can be expressed by the value cosθ, where θ is the angle shown in Fig. 1. However, this theory can not exactly express the pattern when the opening is equivalent or small in comparison with the wave-length and θ approaches 90°. In order to present a practical calculating method, we studied this problem by means of wave acoustics on the basis of the following assumptions; (1) The distribution of particle velocity on an operating is primarily determined by the incident wave. (2) The opening can be regarded as a secondary sound source. (3) The opening is located in an infinitely large rigid wall. (4) The thickness of the wall is negligible in relation to the opening and to wave-length. Based on this analysis, the velocity potential through the opening in the far field, when a plane wave falls upon the opening, can be expressed by Eq. (5) for a rectangular opening and by Eq. (6) for a circle one. The directivity through the opening of the diffuse sound field can be expressed by Eq. (8) with regard to the acoustic power. The following conclusions are obtained as a result of this study; (1) The directivity pattern given by Eq. (8) satisfactorily accords with the experimental results (Fig. 4, 5). (2) The limit of Eq. (8) as frequency tends to infinity, approaches the value cosθ for a rectangular opening (Eq. (24), (25)) and the value cos^2θ for a slit-shaped opening in the plane including the long side of the slit (Eq. (32), (33)). (3) Measured correlation coefficients on the opening accords with the theoretical value derived by Cook, from which it is confirmed that the assumption (1) mentioned above is applicable (Fig. 6). (4) Based on the transmission factor derived by Gomperts, it is conceivable that the sound pressure in the normal axis of an opening can be approximately estimated by means of geometrical theory over the whole frequency region, and this phenomenon is experimentally observed (Fig. 7). (5) Practical calculation charts for the directivity are presented (Fig. 8).

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In order to obtain a relation between subjective measures for room sound effects and physical values, when time and space structures of early reflection sounds in an auditorium are varied, we conducted hearing tests for excellence of sound in the sound field simulated by a sound synthesizing system. In this paper, procedures and results of multi-variate analysis of the psychological scales obtained from the subjective assessments and those of the physical values are presented. For the original sound for the hearing test, string music played in an anechoic chamber was used. Test sounds from the original were reproduced in pairs through a digital delay unit, attenuates, and loundspeakers set in the anechoic chamber in accordance with test conditions. Fig. 4 gives the arrangement of the loudspeakers. For the test conditions, time-delay and the reproducing level of sounds from the loudspeakers S_2〜S_6 were controlled, so that the number of reflection sounds within 85 ms of time delay was 2〜8, and that of the conditions was 54. Other physical values at the listening point were as follows. (a) Ratio of early to reverberant sound energy: 0. 77〜2. 74, (b) ratio of front to back sound energy: 3. 03〜5. 04, and (c) listening sound pressure level: 83. 3〜86. 3 dB. The hearing test was carried out on these 700 or so pairs of stimuli compiled at random, with two engineers selected as listeners. Data of the assessment were constructed in spaces from dimensions 1 to 5 by means of Kruskal's multidimensional scaling. However, the configuration converged in 3 dimensions under the experimental conditions. Values corresponding to each configuration axis in 3 dimensional space were named as subjective measures I, II, and III respectively, and the correlation between these and 10 physical values was studied. In order to extract the physical values corresponding with 3 of the subjective measures as independently as possible, the varimax method was used. That is, coordinates of the measures were rotated in a space of 3 degrees of freedom, and by multivariate analysis of the rotations measured and the physical values, structure vectors of each composite variable, which were orthogonal to each other, were calculated. As a result, excellent correlations were obtained for the following: (a) Subjective measure I; ratio of early to reverberant sound energy and level of reflection sounds from the front horizontal directions of the listener, (b) subjective measure II; listening sound pressure level and number of reflection sounds, and (c) subjective measure III; ratio of front to back sound energy.

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This paper aims at seeking an acoustic index which can be correlated with the most important subjective quantity evaluations and architectural conditions and physical quantities by performing hearing tests of music through sound reproduction of a dummy head recording in actual auditoriums in order to examine acoustic design criteria of auditoriums. Thirteen multipurpose auditoriums were examined each containing 700 to 1500 seats, with a large variety of shapes and acoustic characteristics. The sound source was an non-directional speaker with a constant output power placed on the stage, emitting music (five types of instrumental and vocal music) recorded in an anechoic room, and the emitted music was recorded by means of a dummy head in the seats of audience. Measuring points were selected in common for all the halls examined, and included two points on the stage, one placed 1 m sideways off the central line with the sound source as the reference point, and others on the grid of 7 m intervals. The acoustic hearing tests were performed by means of a capacitor-type headphone. The following were the items of subjective evaluations; loudness, quantity of reverberation, spatial impression, quality of reverberation, brilliance, definition, proximity and preference that is an overall evaluation of these. Hearing tests were performed by pair comparison between the 13 halls at two representative points, and between 6 halls having various and acoustic characteristics at their respective 24 to 26 points. The results revealed a factor structure of the items of evaluation between the halls, in which the quality of reverberation and the spatial impression were indicted along the I-axis, while the definition and proximity were shown in reverse correlation with these along the I-axis. When a stage enclosure was installed, the brilliance can be shown along the I-axis, adding a qualitative factor to the I-axis (Fig. 3). The results of the multiple regression of the hall specifications in relation to the preference indicated that the preference can be explained to large extent in terms of hall width and volume (Eq. (1)). With regard to the quantity of reverberation good correlation was found in the initial sound decay index and reverberation time in the middle and high frequency ranges (Table 6). In the factor structure of the subjective quantities in the same hall, the larger the hall, the greater the effect of sound volume (II-axis) on the criteria of the preference and quality of reverberation(Fig. 5). There was good correlation between the initial sound decay index and the quantity of reververation in the relationships between the subjective and physical quantities (Table 7). The above-mentioned results have revealed that "Centre time" T_s, in particular among the initial sound decay indices, has the most stable correlation with the difference between the position in the same hall and that between different halls with regard to the quantity of reverberation.

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