Acoustic pollutions are now as important social problems as air and water pollutions. In our social life various complex sound fields due to acoustic sources of more or less random nature are produced. Therefore, in this paper, these noise sources are characterized by stochastic time functions and the propagation of noise radiated by them is considered by using correlation analysis. At first radiated sound fields due to stationary or nonstationary random point source, fixed in space, are considered. Power spectrum, mean square average and correlation funcutions of the fields are expressed in terms of the corresponding quantities of the source and transfer functions. Then, we discussed the sound field radiated by a random point source moving at a constant velocity which simulates a car, an aircraft etc. Both subsonic and supersonic cases are considered. Next we studied a sound field radiated by a flow of random point sources simulating a road traffic. The mean square values of the field is expressed as a function of now density, velocity and power of each point source as well as distance from observation point to the flow. The above considerations may give some basic informations on propagation of noise and be useful to establish a criterion for noises.

抄録全体を表示

In our privious paper, noises emitted by random point sources were studied in several cases. Noise sources such as a train, a car etc. , however, are more realistic to regard as line or surface sources than to regard as point sources. Noises emitted by a random line source with finite or infinite length were studied in this paper. The line source subject to the stationary random process is fixed in space or in motion with a constant velocity. Space and time correlation and the mean square value of the radiated sound were obtained by using an auto-correlation function and power spectrum of the source for the following cases. (1)Each point on the line source behaves in the same way. (2)Each point on the line source quite independently. (3)Behavior of each point on the source is transmitted with a constant velocity along the source. It has been confirmed that the radiated sound field is greatly influenced by the difference in correlation between behaviors of points on the line source. This study is considered to give some basic information on propagation of noises from a random line source.

抄録全体を表示

In social environment there are various kinds of sound fields emitted by randomly distributed acoustic sources. In our previous paper we studied a flow of random acoustic point sources moving on a straight line as a simple model of road traffic noises, and derived space and time correlation of acoustic power observed at different points in the radiatted sound field. To begin with, in the present paper, simple approximate expressions for probability densities of PWL observed at a point surrounded by random distribution of point sources were derived by using the law of distribution of the nearest acoustic sources neighbor. The probability distributions are given in Eqs. (2. 11)〜(2. 13) and shown in Fig. 1. These curves make a parallel shift to the higher level side with an increase in the average density of point sources. These relations are given in Eqs. (2. 14)〜(2. 16). Especially Eq. (2. 14) for linear random array of point sources is in good agreement with the experimental formula representing the relation between a noise level near a road and trafic volume. Effects of an ambient background noise on the probability distributions of a direct sound were also studied and are shown in Fig. 2. It has been confirmed that a background noise usually has a great influence on the lower level side and raises a lowest level, but has little influence on the higher level side. Next we derived an accurate expression for the probability distribution of PWL observed at a point on a linear random array of acoustic sources. The results are compared with those of the approximate expressions mentioned above and shown in Fig. 3. When an observation point is not on a linear random array of sources as shown in Fig. 4, an approximate expression for the probability density of power transmitted to the point was also derived using the saddle-point method. The results are shown in Fig. 5. These statistical considerations on sound fields emitted by random distribution of point sources are considered to be usefull for estimation and physical understandings of traffic noises etc.

抄録全体を表示

In this paper a model for panel vibration type sound absorbing materials is prepared, and the effects of some physical quantities of panel materials, the depth of an air-space backing and the acoustic impedance of a rear wall on sound absorption characteristics of the system are studied through theoretical analysis. The model for the panel acoustic system adopted in this paper has a cylindrical form including a circular panel with its circumference clamped (see Fig. 1). In Fig. 1 the plane sound wave travels in the plus z-direction and is normally incident on the panel surface. It is assumed that the acoustic impedance of the panel surface in a static state and that of the inner surface of the cylinder are both infinite, while the rear wall has a finite acoustic impedance. In addition it is presumed that the modes of vibration other than axisymmetric vibration with circular nodes are not allowed for the panel. In theoretical analysis of the above system, we begin with solving an equation for forced vibration of the circular panel. Then the wave equation in the cylindrical region on the left side of the panel (Region I), and the equation on the right side of the panel (Region II) are solved. Boundary conditions are expressed by Equations (19), (20) and (21) for Region I, and by Equations(25), (19)' and (20)' for Region II. As a result Equation (22) for Region I, and Equation (26) for Region II are obtained. On the other hand, Equation (30) is derived on the assumption that the driving force exerted on the panel arises from the pressure difference between both sides of the plate. Multiplying both sides of Equations (22), (26) and (30) by the m-th normal function for vibration of the circular panel with its circumference clamped, for density integration all over the panel surface results in Equation (37) for obtaining a vector C with an element C_n, which is the amplitude of the reflected wave of the n-th mode of vibration propagated in Region I. If these C'_ns are known by numerical calculation, the sound absorption coefficients of the system can estimated. Comparisons between calculated values and measured values by the standing wave tube method of the sound absorption coefficients of circular plates of vinyl chloride are presented in Fig. 4, and Fig. 5. Since these figures show good agreement, we next study the effects of the modulus of elastidty, thickness, density and loss factor of panel materials, the depth of an air-space backing, and the acoustic impedance of a rear wall on the sound absorption characteristics of the system by the same method of calculation. The sound absorption characteristics are expressed by three quantities defined as follows. (1) Relative frequency deviation Δf=(f_<res>. - f_<pro>. , where f_<res>. is the lowest resonance frequency of the system and f_<pro>. is the lowest natural frequency of the panel. (2) Sharpness Q of the lowest peak in the sound absorption characteristics. (3) Absorbed energy A. This is the energy absorbed in the band width of 400 Hz around the lowest resonance frequency of the system. The results are as fol1ows : (1) There is a linear relation between the modulus of elasticity, and Q and Δf, but A shows a constant value independently of the modulus of elasticity (see Fig. 6). (2) Q increases but A decreases with an increase in the thickness of panel material. When a panel is thin, however, Q and A change little Δf varies notably with a change in the hickness of panel material, that is, the thinner a panel is, the larger Δf is. This may be attributed to the movement of the second peak of the sound absorption characteristic toward the lower frequency region with the lowest peak remaining nearly stationary, thus getting these two peaks to get closer with a decrease in the thickness of a panel (see Fig. 7). (3) Δf and Q are independent of the density of panel material (see Fig. 8). (4) A

(View PDF for the rest of the abstract.)

抄録全体を表示

There are many problems which can be treated as forms of finite amplitude wave motion, e. g. , shock waves and radiation of large amplitude ultrasonic waves, but no adequate analysis of these problems exists since they are nonlinear phenomena. In this paper, finite amplitude wave motion in a closed pipe is investigated as one example of a finite amplitude problem. The flow of gas in the pipe is assumed to be a one-dimensional, unsteady flow. When the cross-sectional area of the pipe is constant, the wall of the pipe is adiabatic and wall friction is taken into account, the continuity equation, the momentum equation and the first law of thermodynamics are written as Eqs. (1), (2) and (3). These equation cannot be solved by analytical methods since they are nonlinear equations. The solution, however, is obtained by means of numerical procedures, i. e. , the characteristics method, since these equations can be combined in the form of a quasi-linear partial differential equation of the hyperbolic type. After the arrangement of these equations, the compatibility conditions along the three characteristics curves in the physical plane is obtained, and these conditions are expressed by Eqs. (5), (6) and (7). Equation (8) gives the definition of the pseudo-Riemann variables, and when wall friction is neglected, this equation gives the Riemann constants. The dimensionless form for the physical properties in this calcu1ation is given by Eq. (10). The process of numerical calculation is performed in a stepwise fashion with a digital computor by solving the simultaneous equations, Eqs. (13-1) to (13-4) which are in a normal mesh shown in Fig. 1. The boundary condition at the open end, in this case, can no longer be expressed as the open end pressure p being equal to the constant reference pressure p_0. Assuming that the in-flow and out-flow at the open end are in a quasi-steady state, the adiabatic energy equation (Eq. (l4)) is applied as the boundary condition. The numerical calculations are performed for two cases with this boundary codition. One is a calculation with the following initial conditions. The closed pipe is divided by a partition across which an arbitrary pressure difference exists initially at the open end, and the partition is suddenly broken. The other is a calculation under the condition of a forcedsinusoidal velocity of constant amplitude at open end. The results of the calculation of the former case are shown in Fig. 2, and those for the latter case are shown in Fig. 3. Fig. 5 shows the Klirrfactor for the pressure histories at the closed end as a function of V^^^-_<amp> for the latter case. These results indicate that the distortion due to nonlinearity becomes visible when the dimensionless velocity amplitude at the open end (V^^^-_<amp>) is larger than 0. 1. Fig. 6 shows the experimental apparatus which is known as a Hartmann generator. Experiments are performed corresponding to the first case of the numerical calculation. The experimental results are shown in Fig. 7, compared with the calculated results, and the agreement is seen to be good. From above results, it is found that the wave motion in the closed pipe should be treated as a finite amplitude wave motion when the velocity amplitude at the open end is larger than 0. 1 times the velocity of sound, i. e. , when the acoustic pressure level in the pipe is higher than 180 dB.

抄録全体を表示

Irregularly spaced arrays have been shown to be useful for wide-band directional sound sources because their highest signal frequency, which is limited by the frequency of the so-called "greating lobe" can be determined independently of the size of source elements and of the total length of the array which limits their lowest signal frequency. However, the procedure of realization of the optimum distribution of source elements has not been satisfactorily developed. In this paper a new approach to irregularly spaced array design is considered. It is based on distributing N individual source elements irregularly to the points which divide the total array length into M equal parts whose length is to be a shorter value than the shortest wave length of the signal. There are (N-1)!/2 arrangements of the source elements for given N and M. An arrangement which shows the maximum side-lobe reduction level may be the optimum arrangement. For N = 4〜6, the optimum arrangements and their side-lobe reductions are shown in Table 2 using ν_<mn> which is the space between the m'th and n'th source elements where the unit of ν value is one-M'th of the total array length. For more general N and M values, the expected value of side-lobe reduction of the optimum arrangement can be estimated. The estimation formula is given as R_<2δ> in eq. (12) and the estimated values are shown in Fig. 11. Finally, the usefulness of this design method is confirmed experimentally using three arrays. Array a) is the irregularly spaced array source (N = 5, M = 7) of which spaces of elements are shown in Table 2, array b) is the conventional uniformly spaced array source having equal total length to array a) and array c) is also an uniformly spaced array of which spaces of elements are equal to one-M'th of the total length of array a). As shown in Fig. 12, array a) can operate over the most wide frequency range because its lower limit is equal to that of array b) and its upper limit is equal to that of array c).

抄録全体を表示