The original infinite theory of Cremer doesn't coincide with experimental results, particularly on the directivity characteristic. By modifying the symbol for radiation angle (Fig. 1), we have Eq. (1) instead of Eq. (2), which means that the radiation angle is much more effective than expected before, and then, the condition of radiation affects the resultant transmission. We tried in this paper, therefore, to modify the infinite wall theory particularly on this feature. In a real wall with finite dimensions the transmitted wave diverges in all directions (Fig. 2), and its intensity I_t depends on the velocity of wall u_w in a certain functional form as I_t=f(u_w), u_w on the pressure of incident wave p_i as u_w=g(P_i) and finally the transmitted energy e_t is expressed by Eq. (4). By the aid of radiation factor λ(ka, kb) for a rectangular wall given by Eq. (12), calculated from the fundamental formula of Lord Rayleigh, Eq. (8), we can arrive at Eq. (11) as the functional form of e_t, and also by utilizing Eq. (3) for u_w from the original theory, we have practical forms of insulation, normalized SPL difference D'_n for single directional incidence and Sound Transmission Loss TL (Sound Reduction Index R in ISO R 140). Radiation factor, usually substituted by λ(ka) for a square wall, has two significant variables, incident angle θand (ka), k=w/c and S_w=(2a)^2 is the wall area. λ(ka) is illustrated in Fig. 4, where the dotted linef or an infinite wall expressed by Eq. (14) corresponds to the 'Abstrahl-Faktor' of Gosele. Curves for ordinary wall tail off from higher value of θ, when (ka) diminishes from infinity, and change completely to a flat characteristic given by Eq. (13), when (ka)<1. It remains rather immutable to θ in ordinary windows, because (ka) is not so large in the lower frequency region (Table 2). Fig. 5 shows also λ(ka) taking (ka) as abscissa, in which it is noticed that the transmission through wall is quite similar to a cone-action of loudspeaker, because (pc)×λ(ka, kb) expresses, refered to Eq. (15), the radiation resistance of vibrating rectangular-board per unit area. Direct application of the infinite wall theory to real walls would be equivalent, therefore, to the assumption that the diameter of cone-speaker would be always sufficiently larger than the wave-length of sound wave. D'_n and TL are defined by Eq. (16) and (20), leading to their theoretical expressions Eq. (19) and (24). Q in Eq. (24) is average of λ(ka, kb) in special directions of incident waves defined by Eq. (23) and calculated in Table 1 for the square wall, which gives the spatial average of D'_n as D'_na in Eq. (26). Figs. 6 and 7 show calculated values of D'_n and TL. Incident angle θhas generally few influence on D'_n, consequently the spatial average D'_na calculated from TL comes in good agreement with D'_n. TL becomes a little larger than the value for the Limp-Wall-Law of A. London, when S_w diminishes from infinity, but only with a slight deviation from it, except when S_w<1m_2. These tendencies in the experimental observations already known would indicate the importance of diffraction in the transmitted wave, and finally the fact that there is approximately no directivity in the behavior of windows would present a practical advantage to experimental works.

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Studies have been made by many investigators to seek for new acoustical criteria in room acoustics by converting echo oscillograms into physical quantities. In making an acoustical design of an auditorium, we obtain proper indices for the shape of the room by conducting an acoustic model experiment. We intend to use effective physical quantities out of the acoustic criteria obtained in the experiment for the actual design of the auditorium. This paper summarizes the results of our study and discussion regarding the relations between the physical quantities and the room shape, between various quantities themselves, and between the physical quantities and the subjective evaluations on the basis of the room distributions of various physical quantities obtained by converting the respective echo oscillograms into physical quantities regarding nine halls of different shapes of room (Fig. 5). We studied the numerical physical quantities regarding the D value (Definition) of the energy volume when the time axis is fixed, the time required for attenuation by 3 dB from the stationary state (T_<-3dB>, Rise Time) and the time required for attenuation by 10 dB (T_<-10dB>, Early Decay Time) as the value of the time when the energy attenuation is fixed, and the center time (ts). As a result, we found that the distributions of the physical quantities in the auditorium in correspondence to the variation in the hall dimensions and shapes tended to vary depending on what point of time of the initial attenuation the physical quantities were evaluated. In other words, the D value and the T_<-3dB> evaluated at a very early time tended to be influenced more by the delicate variation in the neighborhood of the measured point than by the difference in the basic shapes of the auditorium, whereas T_<-10dB> evaluated in a later point of time in the initial attenuation tended to show relatively more clearly the difference due to the basic shapes of the auditorium (Fig. 6). For this reason, it was considered better to use T_<-3dB> for observing the difference in the basic shapes of an actual auditorium, and that it would be more appropriate to evaluate the difference in detailed parts in the physical quantities at a shorter time point. Moreover, we observed that various physical quantities in the same echo oscillograms were often quantified in different directions even when evaluating the same type of subjective quantities (Fig. 7 and Fig. 8). Thus, considering these findings, we found that when the initial attenuation characteristic was represented by the bend b=T_<-10dB>/T_<-3dB> (b_0=3. 33 for exponential attenuation), this tendency appeared if b/b_0 was deviated greatly from 1, and that the respective physical quantities showed relatively constant relations when b/b_0 was used as the correction value (Fig. 10). Taking the foregoing into consideration, we performed a hearing test on the subjective reverberation which is one of the principal subjective quantities in room acoustics by the pair comparison method. As a result, we found that regarding the specimen sound sources of a wide range of reverberation time (RT=1. 1〜1. 6 seconds), such physical quantities requiring a relatively longer time for observation as the reverberation time, the time required for attenuation by 20 dB from the stationary state, and the center time were well correlated, and the subjective reverberation was basically evaluated by the length of the reverberation time. On the other hand, regarding the echo oscillograms having the same degree of reverberation time, we found that such physical quantities determined in the earlier initial period as the ratio of the energy up to 100 ms〜150 ms to the total energy and the center time ts were well correlated (Fig. 11). It is to be noted that the center time ts which in particular represented the time distribution of energy in all the echo

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