The measurement method for obtaining the system dynamics of a loudspeaker in the form of the system function is discussed assuming that the loudspeaker is a linear time invariant system. Generally, in a linear time invariant system the relation between the input to the system and the output from it can be represented by its impulse response or its system function. The measurement method of the system function in a frequency domain has some characteristic comparable to these of the impulse response in a time domain. Namely, since the stationary continuous signal is used as the input test signal, the measurement can be performed without the confluences of loudspeaker non-linearity and the measuring system noise. On the other hand, the difficulty of phase measurement comes into question. In this paper, since there exist only a relation between the phase characteristic and the group delay characteristic, the theory of the simultaneous measurement for the amplitude frequency characteristic and the group delay frequency characteristic is investigated to obtain the system function. In this case, the balanced modulated signal as indicated by eq. (2) is used for the input test signal. When the input signal f(t) is introduced into the system, its response signal g(t) is indicated by eq. (8). Using the assumption of eq. (9) and approximation of eq. (10), appearing in the result, g(t) can be represented by eq. (11). Accordingly, A(ω_0) can be measured by comparing the maximum envelope amplitude of g(t) with that of f(t), using the block diagram as shown in Fig. 1 (a). Furthermore, τ(ω_0) can be measured by comparing the time delay between the envelope of f(t) and that of g(t), using the block diagram as shown in Fig. 2 (a). By means of these measurements for all measurable frequencies, it is posiible to obtain the system function. Next, the possibility of the above measurements, in case the amplitude characteristic is subjected to wide fluctuations as a loudspeaker, is investigated. In such a case, the response signal g(t) for the input test signal is indicated by eq. (14), and its waveform is shown in Fig. 5. In this case, since the maximum envelope value of A_1 and A_2, it is seen that A(ω) can be measured with good approximation by selecting a sufficiently small Δω. When the envelope waveform of g(t) is analyzed into its frequency components by using the Maclaurin expansion, eq. (17) and eq. (18) are obtained. As is clear from these equations, since the time delay of the 2Δω component of g(t) is equal to τ(ω_0) as compared with that of f(t), the measurement of τ(ω) presents no problem. The measuring apparatus for the system function was made, based on the theory of the simultaneous measurement for A(ω) and τ(ω). This fundamental block diagram is shown in Fig. 7. The parts for the A(ω) measurement and τ(ω) measurement are used respectively in the block diagrams shown in Fig. 1 (a) and Fig. 2 (a). Measurement results are converted from analog values to digital values and can be used as input data of a digital computer by OFF-LINE intermadiated by punched papaer tape. Fig. 8 (a) and Fig. 8 (b) are one example of measurement results. In addition, echo distortion caused by group delay characteritic has been taken into consideration.

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One of the heuristic methods to improve the diffuseness of the sound field in a reverberant room is to place obstacles in the room. Scattering of sound by the obstacles makes the field complex and diffuse as a whole. The field near the obstacles, however, does not approach to the diffuse sound field, since the field is strongly constrained by the boundary conditions on the obstacles. In order to clarify these basic problems in room acoustics, here the influences of an obstacle on the diffuse sound field in which the obstacle is placed were investigated. Theoretically we assume for simplicity that the diffuse sound field is equivalent to the random incident plane waves on the object. Space correlation function of the sound pressure around the sphere shown in Fig. 1 was derived as Eqs. (13)〜(18), and the mean square sound pressure is given by Eqs. (19)〜(22). Similarly, the mean square sound pressure at an observation point around the cylinder shown in Fig. 2 was derived as Eqs. (27)〜(30). In Fig. 3, sound pressure increase on the surface of a rigid sphere due to random incidence of plane waves is compared to that due to incidence at some fixed angle of plane waves. The pressure increase due to random incidence gives the average characterisitcs of the pressure increase due to the incidence at various specific angles. Comparison of the caluculated and the measured increases of sound pressure level on the surfaces of a rigid sphere and a rigid cylinder due to random incidence of plane waves is given in Fig. 4. The curves monotonously increase and approach 3 dB as frequency parameter ka becomes large. For small ka, both curves shift to 0dB, although the curve corresponding to the rigid cylinder shifts slowly as compared with that corresponding to the rigid sphere. The variations of relative sound pressure level along the radial direction of the above described objects in a reverberant field were also predicted and compared with the measured ones. The results are shown in Figs. 5, 6, 9 and 10. The block diagram for the experiment is given in Fig. 8. The measured values are in good agreement with the predicted ones. The relative sound pressure level in these figures converge to nearly 0 dB as the observation point moves away from the object by about one diameter. Accordingly, the field more than one diameter apart from the rigid surface of an object seems to be diffuse similarly to the original incident field. The result is also supported in case of the field around a soft sphere (Fig. 7) and is expected to hold for the field around any object in a reverberant room.

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In general, it is well-known that the distribution function within a higher fluctuation range can reflect the evaluation of human response and the individual characteristics of noise and vibration, so that it is more important than that within a lower fluctuation range in the field of the evaluation of industrial and road traffic noise. From this point view, this paper provides the method of statistical treatment of random noise or vibration which is suitable to the estimation of the level distribution within a higher fluctuation range and a simplified evaluation procedure of the higher L_α sound level, by introducing the idea of conditional distribution function. In the previous paper, we have reported on some trials of the statistical treatment for the digital level fluctuation of arbitrary random noise or vibration, when the random noise or vibration with the level, Z, of arbitrary distribution type is considered as a sum of two different random processes, X and U, with the digital level based on the naturalinternal structure or analytically artificial classification of fluctuation. Let us now introduce an arbitrary function, (Z), and consider its expectation value, Eq. (1). Equations (3) and (4) can be obtained by using the backward Newton's interpolate formula. Our main problem is how to derive the probability function, P(Z), in the difference form expanded into series based on the statistical informations of X and U. After somewhat complicated calculation, we obtain the two expressions expanded into series, Eqs. (11) and (13), when X is statistically correlated with U;Eqs. (14) and (15), when X is statistically independent of U. Though the theoretical development in this paper seems to be similar to the previous method, we would like to emphasize the fact that the resultant expressions are different forming striking contrast with the previous results. Namely, in comparison with the probability density or distribution functions in the previous paper, Eqs. (14) and (15) are the theoretical expressions based on the forward difference formula, being different from the previous statical treatment. Therefore, these theoretical expression are very suitable to the estimation of the level probability distribution within a higher fluctuation range. We have experimentally confirmed the validity of our theory by means of not only digital simulation, but also the experimentally observed city noise data given by Dr. Morita and the road traffic noise data in Hiroshima City. The result of experimental study are shown in Figs. 1 through 7. Equation (22) is the conditional distribution expression that is introduced for the purpose of the effective processing of experimentally observed data (see Fig. 4). With the aid of this expression, the long time level distribution can be easily predicted from the short time level distribution within the higher fluctuation range by using only a part of all observed data. The corresponding experimental results are shown in Figs. 6 and 7. The above statistical treatment is characterized by the following points:(1) The resultant expression are given in the form of the difference type, so that the frequency distribution, P_(X), can be utilized keeping the experimentally observed data in their crude numerical form without making continuous level fitting;(2) In the special case when the level width h=d, approaches to 0, the above theoretical expression exactly agrees with the expression reported previously in the continuous level form;(3) Since the present theory is suitable to the stimation of the level distribution within the higher fluctuation range and the prediction of the higher L_α sound level, the proposed statistical treatment can be used to such random noise and vibration showing various distribution types on the basis of the flexibility and universal validity of the theoretical expression;(4)By using the conditional distribution function

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Most of the noises generated in daily life are fluctuating in both level and frequency. It is important for a measure of such fluctuating noises to reflect subjective judgment, to be applied to any kind of noises, and to be easily calculated. L_<eq> and L_α are often used as the measures of noises, but, in actual noises, both are apt to take similar values, and it has not yet been decided which is more suitable. There, in the present study, two experiments were conducted in order to make clear the propriety of L_<eq> and L_α as the measure of traffic noise. Pink noise was used as stimuli, the level of which was changed simulating road traffic noise so that the values L_<eq> and L_α might be different (Fig. 1 ・Table 1). The duration was about 30 sec. These stimuli were generated with a noise generator, and recorded on magnetic tapes, after the level and time were controlled by Programmable Sound Control System. In the experiment, they were reproduced, and presented to subjects through an amplifier and a loudspeaker in the sound proof room. In Exp. I, the method of magnitude estimation was used. Subjects judged the loudness of each stimulus assigning freely a number which seemed to reflect the loudness. They were able to use any number as they liked except negative. In Exp. II, the method of subject adjustment was adopted. Steady-state pink noise with same duration was used as the comparison stimulus. Subjects controlled the level of the comparison stimulus by themselves, hearing and comparing two noises a number of time, and carried out the matching of the loudness. Both noises were repeatedly presented with 30 sec silent intervals until the subjects finished the matching. Correlation was examined with coefficient of correlation and standard error between subjective judgment and physical values for estimation-L_<eq>, L_α(L_5, L_<10>, L_<20>, L_<50>) and the loudness level based on Stevens' Mark VI(LL_E, LL_P, LL_5, LL_<10>, LL_<20>, LL_<50>). LL_E is the loudness level calculated from the energy mean of each octave band, LL_P is the energy mean of the loudness level calculated every 100msec, and LL_α is the loudness level calculated from L_α of each octave band. As a result, L_<eq>, LL_E and LL_P, which are based on the energy mean, showed higher correlation with subjective judgment and smaller standard error than L_α and LL_α in both experiments (Table 2). Consequently, the energy mean seems to be more suitable than the statistical values, such as L_α, for dealing with level fluctuating. As for the frequency weighting, both dB(A) and Mark VI treatments showed good correspondence with subject judgment, but taking the trouble for calculating LL into account, it may be concluded that L_<eq> is more suitable for the assessment of traffic noise.

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Wind speed distribution plays an important role on the propagation of sound outdoors. Hitherto, its effects have been explained unsatisfactorily by sound ray and shadow zone theory. The author proposes new method of caluculation which is based on Fresnel's theory in optics and the phase change of sound waves by wind. If there is no wind, Fresnel's theory says that sound field at R(Fig. 1) can be calculated by integrating secondary waves from the surface elements on the reference sphere. Lunar portion (Fresnel's lune in Fig. 2) can be taken as the surface element, then wave element is given as eq. (1). Integration of eq. (1) makes Cornu's spiral(Fig. 3), from which wave field at R can be determined. If there is wind speed distribution, it is assumed that the wave element from the lunar portion becomes the form of eq. (2), which means wind affects only on the phase of secondary waves and not on the amplitude. This is based on the idea that wind speed is small as compared with sound speed, so that wind effect should be small. But the phase change is accumulated with distance, therefore the effect of wind on the phase should not be ignored in long distance. Integration curve of eq. (2) is shown in Fig. 5, in which wind distribution is assumed as w_0(x/x_0)^<0. 33>, and the reference sphere is divided into 1 cm step from 0 to 20 m height. If wind blows in the same direction as sound(Fig. 5(b)), the distance from the starting point of vector to asymptotic point (center of shrinking spiral) is nearly equal to that of no wind case(Fig. 5(a)). This means sound amplitudes are nearly equal in both cases. If wind blows against sound(Fig. 5(c)), the distance becomes small and attenuation becomes large. The discussions above stand if there is a screen as shown in Fig. 6, but are not exactly correct when there is ground surface as shown in Fig. 4. Fig. 6 should be considered as the approximation of Fig. 4. In the computation, multiple reference spheres are considered(Fig. 8), which are the approximation of the case in which there is ground surface as shown with a broken line in the figure. The distance between the reference spheres should be so small that only the phase of elementary waves changes and the amplitude does not. Secondary waves from Q to P is given by eq. (4). The column vector composed by the waves at each element of different height on (i+1)-th reference sphere is calculated according to eqs. (5)-(9) from the similar vector on i-th sphere and the phase shift caused by wind. These are the fundamental equations for calculating wind effects. Several computation results are shown in Figs. 9-12. In most cases, the wave elements on reference spheres are considered from 0 to 40 m height at 5 cm intervals, and the distance from one sphere to the next is 20 m. Sound source height is 1. 4m, and attenuations at various receiver height are plotted. It is observed that when wind blows against sound, large attenuation occurs at low receiver position and long distance. At heigh receiver position, attenuations are almost equal to that of geometrical spreading(inverse square law). As sound wave length becomes shorter, attenuation at low position becomes larger. Even there is no wind, attenuation occurs at low receiver position. This is the effect of diffration by multiple screens, and approximates the effect of fully sound-absorbing ground. This paper concerns only one aspect of sound propagation outdoors. Many other factors should be considered in practical problems.

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