Until the present, various expressions of a probability distribution function, which play an important role in the evaluation of road traffic noise, have been presented. We firstly derive a new universal expansion expression of multivariate joint probability distribution with both discrete and continuous random variables, based on the Lebesgue's decomposition theorem. We show that our expressions, as special cases, agree with Kurze's probability expressions introduced for the road traffic noise such as “semiinfinite source line, ” “short source line” and “very light traffic.” As one example, after choosing a combination form of Gaussian and gamma distribution functions as the first term of our expansion expression, we confirm experimentally the validity and the effectiveness of our theory not only by means of a digital simulation technique but also by applying to actually observed road traffic noise data.

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The present study provides the result of an attempt to analyze statistically the performance of articulatory parameters to express formant frequencies. A quadratic curve is computationally fitted to the sampled points on the cineradiographic trace of the tongue profile to express the tongue position either on the coordinates relative to the mandible or relative to the maxilla. The tongue position is defined by the specific point in the quadratic curve on its axis just R₀ apart from the vertex, where R₀ is the mean radius of curvature at the vertex. The protrusions and aperture of the lips are reduced into a single parameter by the principal component analysis and used as an articulatory parameter. The mandible opening and the larynx height are also adopted as articulatory parameters. The first three formant frequencies are extracted by the LPC analysis from synchronously recorded speech sounds. Stepwise regression analysis of the formant frequencies is conducted on the various subsets of those articulatory parameters and the performances of the polynomial functions of those parameters to express the formant frequencies are examined. The result shows that the four polynomials of the articulatory parameters are effective to express the formant frequencies.

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Behaviours of the Bragg maximum and minimum in ultrasonic light diffraction, as well as the fine structures in dependence on the angle of incidence are calculated by the normal mode theory and partly by the Phariseau formula as the high frequency approximation of the plane wave theory-Raman-Nath difference-differential equation method. The Phariseau formula proved to be a good approximation in a certain range of the parameters. A modification of the Phariseau formula for microwave frequencies is proposed.

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A method that can be applied to the radiation problem of a convex or a concave radiator in an infinite baffle is described. This method utilizes the least square error method, and allows the radiator to take almost any kind of axisymmetric shape even though the accuracy of the result depends on the shape. The frequency responses of the onaxis sound pressure are calculated for three cases of the radiator shape, a convex dome, a concave dome, and a combination of a truncated concave cone and a convex dome at the center. The accuracy is confirmed by comparing the results obtained by the present method with those obtained by previous methods by the present authors. Three error indexes are suggested for an estimation of the accuracy of the results.

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A theory of sound propagation based on Niessen's method is developed. The velocity potential at a given point above a boundary is expressed in the form of surface integral on the boundary. The advantage of the theory is that it is applicable not only to a homogeneous plane surface but also to a surface with irregularity or a composite surface of different kinds. Theoretical examinations are made in three cases, i. e., a boundary of perfect reflection, a boundary of finite impedance and a boundary of finite impedance with irregularity. In the last examination, it is assumed that the boundary is almost flat but has some concaved portions distributed with a certain pattern. On this assumption, the theoretical result is found in good agreement with the experimental result measured over a turf-covered ground. A way of applying the theory to the case of a composite surface is also described. In connection with the theory, the strict mathematical formulation of Huygens principle is given.

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The early reflections in the sound field of an auditorium have important roles in the impulse response and transfer function. The practical calculations are already shown for the first reflections from the boundaries and compared with measured reflections in good agreement. In this paper, the estimation of the multiple reflections between rigid plane panels is treated, based on these. When a panel is small, or the distance between a point source or a receiving point and the panel is large, the multiple reflection of a boundary wave cannot be neglected compared with that of a geometrical wave. Because the first reflection of a rigid plane panel has separate geometrical wave and boundary waves, the multiple reflections between them are obtained by those of each wave. Since a boundary wave is explained as the contribution of lined point sources with directivity on an edge, its multiple reflection is calculated as their geometrical reflection and their boundary waves of a reflecting panel. This calculation method is applied to two rigid plane panels which have a broad angle in between, and two which are in parallel. The calculated results are compared, in the time and frequency domains, with measured values in good agreement.

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