The mass law of sound transmission through an infinite single partition is well known, and the mass law for oblique incidence has been derived on the assumption that the partition consists of particles not connected with one another. Cremer pointed out that oblique incidence sound transmission deviates considerably from the mass law above the coincidence frequency, where the inertia of the partition and its stiffness cancel each other. However, there is a resonance contribution to transmission for a finite partition and the transmission characteristics above the critical coincidence frequency f_c are different from those below f_c for any incidence of angle, since the sound radiation of flexural vibration depends on the frequency. Consequently the relation between the vibration and the reaction of the air is very important, and in order to analyze transmission through a finite partition, it is necessary to take account of its stiffness, internal loss, shape, size and surroundings in addition to its mass. This paper presents an analysis and a physical interpretation of transmission of a normally incident plane wave through a circular plate set flush in an infinite rigid baffle, where the internal damping and the reaction of the air to the vibrating plate are taken into account. The theoretical results shown in Figs. 3〜7 are as follows:1)The plate vibrates in such a way that a piston motion and a flexural motion are superposed. 2)The transmission loss T. L. at anti-resonance is nearly equal to that of a circular piston plate, where the amplitude of the flexural vibration is relatively small. 3)The deviation from the mass law occurs at the resonance point because the amplitude of the flexural vibration is very large at this point, and the flexural vibration radiates sound below f_c less than the vibration of an infinite piston does. The deviation for a plate with clamped edges is a little greater than for a plate with supported edges, and the deviation is generally noticeable above f_c when the flexural vibration is damped by the internal loss rather than by the radiation resistance. 4)At lower resonance frequencies, T. L. of the plate with little internal loss becomes apparently negative, which indicates that the equivalent transmission area is larger than the geometric area of the plate by the diffraction effect. 5)At frequencies slightly below the lower resonance frequencies other than the first one, T. L. becomes considerably great, because the flexural vibration cancels the sound radiation of the piston vibration. As a practical illustration, the measured transmission loss of a steel plate with and without attaching a damping material, and the vibration level difference between those two are presented in Figs 8 and 9.

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In the previous paper(this Journal 25(3)1969, p. 122), the author shown that the characteristics of an expansion chamber of a muffler in the distributed constant range are explained in terms of the equivalent open-circuit transmission admittance Y_f of the chamber. In this paper, by analyzing Y_f obtained from the solution of wave equation, the characteristics of the cylindrical chamber of the expansion chamber type muffler are investigated and are compared with the results of experiment. The solution of wave equation in the cylinder, Fig. 2, is obtained under the condition that the input opening is regarded as a circular piston and the output opening is closed. If losses are negligible, the sound pressure on the output-side plate of the cylinder is given by Eq. (21)in the case that the input opening is co-axial with the cylinder, and a rough approximation becomes to Eq. (26)in the case of non co-axial. Typical curves of the first three terms of Eq. (21)are shown in Figs. 3 and 4. In case of a long cylinder, only the first term appears in the region ka&ltλ_&lt01&gt=1. 2197π as Fig. 3, and Y_f becomes to Eq. (23). But in case of a short cylinder, the first and second terms must be considered even in the region ka&ltλ_&lt01&gt as shown in Fig. 4. In the region ka&gtλ_&lt01&gt, the sound pressure on the plate is considerably high, and so |Y_f| is small and the noise reduction may not be expected so much. In general, the effective upper limit for noise reduction is regarded as ka=λ_&lt10&gt=0. 5861π in the case that the input and output openings are both non co-axial, and it is regarded as ka=λ_&lt01&gt in the other cases. In term of frequency, they are shown by Eqs. (27)and(24)respectively. When the loss at the wall of the cylinder is considered, the approximate expression of |Y_f| in the effective frequency range is given by Eq. (36)assuming that the loss is not so large, where R_0, R_l and R_a are the acoustical resistance densities of the input-side plate, the output-side plate and the side wall of the cylinder respectively. It is obvious that the loss makes the minimum value of |Y_f| larger. The measured upper limit frequencies are in good agreement with Eqs. (24)and(27)as shown in Figs. 7, 8 and 9, and Fig. 8 shows that a very short co-axial chamber acts such as a resonator. The relationship between the upper limit frequency and the diameter of the cylinder is shown in Fig. 10. As for the effect of the loss at the wall of the chamber, the results of measurement are larger than the results of calculation as shown in Figs. 12 and 13. But it becomes clear that the loss at the wall compensates the dips of the characteristic curve of |Y_f| caused by the resonance in the axial direction.

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Noise reduction ΔL by an acoustic barrier for straight line source is treated by reduced scale model experiment. The line source used in the experiment has 3. 8m in length and radiates a test noise mechanically. The line source is an incoherent line source. Sound attenuation by a semi-infinite acoustic barrier in a free field was obtained experimentally about this line source. The results were plotted about the relation between ΔL for line source and the Fresnel number N, where N is given by N=2δ/λ and δ is the maximum path-length difference in this case. All experimental values spread in a relatively narrow range, and we can obtain a curve on the average(Fig. 12). This curve shows values lower than those of Maekawa's data, by 3〜5dB which were presented for a point source, and is similar to Rathe's experimental values, which were measured near the tracks of a railway line. In addition, our curve shows a similar tendency to the curve calculated by Kurze and Anderson about an incoherent line source. It was proved by this study that the noise reduction ΔL for a line source can be obtained approximately as the sum of individual ΔL's for sound emanating from a few points on the line source. It may be quite well to consider that the figure providing a relation ΔL vs. Fresnel number N is applicable for design of a barrier for traffic-noise(e. g. coming from cars or trains).

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In order to investigate the effects of high speed train noise, we made a social survey of the community response along the New Tokaido Line and the New Sanyo Line in July of 1972. Though the number of samples were only 424, data showed little internal inconsistency and reasonable results were obtained. The New Tokaido Line was opened to traffic in September of 1964, covering 515 kilometers'distance between Tokyo and Osaka in three hours and ten minutes at the maximum speed of 210 km/hr. The New Sanyo Line in turn was opened to traffic in March of 1972, covering 161 kilometers'distance between Osaka and Okayama in an hour at the maximum speed of 210 km/hr. More than half of the railroad tracks in the New Tokaido Line is constructed on a banking roadbed, while most part of the New Sanyo Line is an overhead railroad built in concrete. In these lines, a train runs in few varieties of formation, at the speed prescribed to every fixed location. Variation of the train noise levels, therefore, is within a few decibels at a given location. The survey was carried as that of informant's life environment, and the questionnaire included 14 items about attitudes to neighborhood, 17 items about reactions to train noise, 5 items about attitudes to noise in general and others. Relations between Likert scales describing direct effects of train noise on the community and peak levels of train noise were obtained;also peak levels corresponding to the neutral point of each disturbance scale were read out(for example, see Fig. 2). In addition, relations between proportions of positive response to disturbance scales and peak levels of train noise were obtained(for example, see Fig. 3). Peak levels corresponding to neutral points and some proportions of positive response are listed in Table 2. Our survey includes"house vibration"(Fig. 4)and"TV picture flicker"(Fig. 5)also. Difference of community responses between New Tokaido Line and New Sanyo Line seems due not only to the difference of habituation but also to the difference of attitudes to noise in general. Train noise corresponding to the same community response is about 10dB higher at the New Tokaido Line than at the New Sanyo Line in WECPNL. Comparing community response to train noise with that to aircraft noise in NNI, values in Table 4 were obtained. Table 5 shows the estimated community response through NRN and observed response in our survey. A percentage of informants who stated high disturbance under lower noise level(about 70dB(A) or less) and percentage of informants who stated low disturbance under higher noise level (about 80dB(A) or more)were both 10 percent or less(Table 6). The former is the percentage of informants who rated the train noise as category 4(such as"I am frequently disturbed")or category 5(such as"I am very frequently disturbed")under the exposure to noise levels below that corresponding to category 2(such as"I am little disturbed")on the Likert scales;the latter is the percentage of informants who rated the train noise as category 2 or category 1(such as"I am not disturbed at all")under the exposure to noise levels above the level corresponding to category 4 on the Likert scale.

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Train noise as a nuisance has begun to arouse an increasing public attention, but there are few investigations on the evaluation of train noise. This study aimed at obtaining a quantitative relation of noisiness to level, duration and rise time of train noise. As a result of the psychoacoustical experiments by using simulated train noise, an expression was obtained and it gave a satisfactory explanation to noisiness. The reliability of the expression was verified in turn through rating experiments by using the actual train noise recorded in a magnetic tape. Relations between this expression and other evaluations are also discussed in this paper. The results obtained here are as follows:1)The noisiness change of train noise caused by the variation of its time pattern is based on the change of its total energy. The rate of noisiness change, however, differs according as the energy change is caused by the change of peak level of noise or by the change of its duration, even if the energy changes are equal in both cases(See Fig. 5). 2)As to noisiness the penalty for doubling of duration Td(10dB down duration time)depends on the peak level of noise. The penalty is 1. 2dB for doubling of duration at 60dB(A) peak level, 1. 5dB at 70dB(A) and 1. 8dB at 80dB(A) respectively(See Fig. 6). 3)As an evaluation index representing the contributions of peak level and duration of train noise in the judgment of noisiness, the following N seems to be convenient and reasonable. N=P. L(A)+(P. L(A)-20)/10log_&lt10&gt(Td) where P. L(A)is the A-scale peak level and Td is the duration. This index gives a satisfactory explanation to noisiness of actual train noise observed in laboratory experiment. 4)When periodical and pulsive fluctuation appears in the peak level, some numerical correction should be made to N. For a fluctuation period of 1 sec or less we obtain +3dB as a correction by another examination. However, further study should be carried out for many cases.

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