It is a well known fact that the original method by A. London derived from the solution of a wave equation is widely used in predicting the transmission loss of a double wall, and further there are many modifications of London's method. But none of the above methods is able to make strictly accurate prediction of transmission loss of sound at random incidence. The content of this paper is characterized by the following three points : (1) Essentially, it is very important to consider not only the resistive factor of the wall impedance proposed by London but also the internal energy dissipation in the cavity, so that a new approach of accurate evaluation is proposed from the standpoint of an equivalent circuit of double wall. To be concrete, an internal dissipation factor in the cavity is reasonably reflected in several circuit constants of the equivalent circuit corresponding to the double wall structure. (2) This systematic theory of predicting the transmission loss of general double wall is given from a wide viewpoint of an equivalent distributed constant circuit of double wall, and is not given from the direct solution of the wave equation. It is noteworthy that the London's basic equation can be directly derived as a special case from our systematic theory. Furthermore, as the other special two cases, the well known Bruel's theory and the evaluation method by the concentrated constant circuit theory are also easily derived from our theory. Thus, the fairly universal applicability of our theory has been verified within the scope of theory. (3) In addition, this paper shows that our systematic method can be extended to the double walls using an absorbent material in the cavity, which is never theoretically investigated. Experimental results found in other laboratories and those of us agreed with our theory satisfactorily.

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A new method of measuring the oblique incidence absorption characteristics of various sound absorbers is described in the first half of the paper. The experimental arrangement is shown in Fig. 2. As shown in Fig. 3, the cross-correlation function between the source signal (1 octave band noise was employed) and the received signal which consists of the direct sound and the reflected sound by a hard board is measured first (a), and then, after the hard board is removed and the phase of the source signal into the loud speaker is reversed, the cross-correlation function between the source and direct sound is measured (b). By adding the latter to the former, the equivalent direct wave φ_&ltx0&gt(τ) is cancelled and the equivalent reflected wave φ_&ltxr&gt(τ) can be obtained. The reflected wave by a test material φ_&ltxs&gt(τ) is also measured in the same way. The complex reflection coefficient of the material H(f) is calculated from Φ_&ltxr&gt(f) and Φ_&ltxs&gt(f) which are the Fourier-transforms of φ_&ltxr&gt(τ) and φ_&ltxs&gt(τ) respectively (eq. (7)). Then, the oblique incidence absorption coefficient α(θ) and normal impedance ratio z_n can be calculated from H(f) by equations (8) and (9). As a check of the validity of this method, measurements of the normal incidence absorption coefficients α(0°) have been made by this method and by the tube method using polyurethane foam of 5 mm thick (U_5) and 10 mm thick (U_&lt10&gt). The results measured by these two methods have been found to be in good agreement as shown in Fig. 7. Subsequently, measurements of α(θ) and Z_n have been carried out in a 1/10 scale model experiment with various types of absorbing materials such as thin porous material (F_0 in Fig. 9, F_a in Fig. 10, F_b in Fig. 11), perforated facings (P_a in Fig. 12, P_b in Fig. 13), Rib wall (R in Fig. 14) and vibrating board (B in Fig. 15). Concurrently, the reverberant absorption coefficients α_&ltrev&gt have been measured by use of a scale model reverberant chamber in which air was replaced by N_2 gas, and compared with the statistical absorption coefficient α_stat (eq. (3) in appendix (1)) or α^*_stat (eq. (4) in appendix (1)) calculated from measured Z_n or α(0°).

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The method of obtaining the reverberant sound absorption coefficient α^*_&ltrev&gt of a plane absorber of porous material for any suspending or mounting conditions without measurement of it in the reverberation room is investigated. Firstly, the space absorber is concerned with. In this case, the side of back space of the absorber is open. The reverberation room may be considered to be virtually divided into two spaces by the absorber and the virtual wall, the space I and the space II (Fig. 1). The sound fields of them are assumed to be diffuse. The reverberation time of the space I is obtained from the differential equations of the energy exchange between two spaces (Eqs. (1)-(7)), and the reverberant sound absorption coefficient of the absorber is given by the well known Sabine's equation (Eq. (8)). Secondly, the absorber with closed back space is concerned with (Fig. 3). Theoretical analysis is the same with the former case except that the area through which the energy is exchanged between two spaces is limited to the surface of the absorber (Eq. (11). When the absorber comes near to the reflecting boundary, it is in the coherent sound field composed of the incident wave and the reflected wave from the boundary. In this case, the results obtained above is corrected by the wave theory considering the interference patterns in the field near the boundary (Eqs. (12)-(16)). The reverberant sound absorption coefficient of a rectangular absorber was calculated numerically as a function of the distance from the boundary for several parameters ; the volume of the reverberation room (Fig. 5(a)), the surface area of the absorber (Fig. 5(b)), the ratio of two neighboring sides of the absorber (Fig. 5(c)), the energy fraction absorbed by the material (Fig. 5(d), Fig. 7(a)), and the energy fraction reflected by the material (Fig. 5(e), Fig. 7(b)). The reverberant sound absorption coefficient corrected by the wave theory was also calculated numerically (Fig. 6). For a layer-built absorber composed of some different porous materials, its effective energy fraction reflected and its effective energy fraction absorbed were derived (Eqs. (17)-(21)). The results obtained are as follows : (1) α^*_&ltrev&gt of the plane absorber can be obtained for any mounting conditions provided that the energy fraction reflected r_m and the energy fraction absorbed λ_d by the material of the absorber are known for random incidence. (2) For a special mounting condition where the plane space absorber is in contact with the reflecting boundary, α^*_&ltrev&gt is given by a simple function of λ_d and r_m excluding the edge-effect and the influence of non-uniform distribution of the kinetic energy. (3) α^*_&ltrev&gt of the absorber with open back space increases up to the maximum value 2λ_d with increase of the distance h from the reflecting boundary. (4) On the other hand, the values of α^*_&ltrev&gt of the absorber with closed back space holds the same value as given in (2) irrespective of the distance h from the boundary. (5) The geometrically calculated values α^*_&ltrev&gt of the absorber in the field near the reflecting boundary being corrected by the wave theory, the fluctuation is added to the values of α^*_&ltrev&gt corresponding to the non-uniform distribution of the kinetic energy in the sound field. This is the same for the absorber with open back space and that with closed back space.

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The present experiments were made to establish a relation between the overall judgment and the instantaneous judgment of the sound which continues over a long period. We have an impression of loudness of sound every moment, at the same time we may judge the overall loudness after some period passed. The overall loudness may be said to be a kind of summation of the loudness at each moment. To find the relation between them is very useful to expect the overall loudness. For this purpose, we have developed a new method, continuous judgment by category. Five subjects with normal hearing ability judged the impression of the sound of each moment using 7 categories from very noisy to very calm by touching one of the 7 micro-switches on the response box corresponding to each category. The stimuli used were nine kinds of road traffic noise with 1 minute duration recorded on a magnetic tape. They were reproduced by a tape recorder and presented to each subject through amplifier and loudspeaker. The responses of the subject were continuously recorded on the recorder. To obtain the overall judgment, two methods were used, semantic differential and the method of adjustment. In the experiment using semantic differential, the subjects were asked to judge the overall impression of the stimuli using 7 categories of three adjective scales, "noisy-calm", "clear-hazy" and "bass-treble", after listening to 1 minute stimulus. As for the method of adjustment, the result of our previous experiment was referred. The findings are as follows : (1) The coefficient of correlation between trials of each subject was so high that method of continuous judgment by category can be said to be reliable. Moreover, the subjective interval between categories was confirmed to be equal by Torgerson's law of categorical judgment. (2) High correlation was found between the sound level and the category scale of continuous judgment of the subjects at every one second (r=. 968). (3) The effect of the preceding stimulus was examined by calculating Leq averaging over 1 sec to 5 sec preceding to the judgment. 2 sec-averaged Leq showed the highest correlation with judgment. This fact suggests that the instantaneous judgment may be affected by the preceding stimulus and determined by averaging the sound level during 2 sec preceding to the judgment. (4) Though the overall judgment showed a high correlation with the average of instantaneous judgment of each changing stimulus, the latter showed a trend to be underestimated in the stimuli composed of 1 or 2 vehicles. This difference could be modified by excluding the judgment of the background noise from averaging. This fact suggests that the overall loudness is mainly determined by the prominent part of signals, and supports our previous finding that the overall loudness of level-fluctuating sound shows a high correlation with L_&lt10&gt or Leq, which are affected by the upper level of the sound. (5) From the findings of these experiments it was found that the overall loudness can be estimated by the instantaneous judgment or the instantaneous sound level. Our new method, continuous judgment by category, can be applied to any stimulus with longer duration. We would like to try it in the future.

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