A theoretical calculation is made on nonlinear attenuation of energy including in an N waveform under comparison with energy dissipation of repeated sawtooth waves. It is found that the attenuation coefficient of energy of N wave estimated is only a quarter of the coefficient of the repeated sawtooth waves, when both waveforms have initially the same pressure amplitude and also the same wavelength at origin located at sound source. Therefore, N wave can propagate longer distance than the sawtooth waves with its pulselength increasing with propagation distance, while the wavelength of the repeated sawtooth waves is invariant. However, the change of the energies of both waves are governed by only a parameter which is given by product of initial slope of straightline between the shock fronts and the propagation distance.

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The composite slow waveguide is an underwater acoustic slow waveguide and has a double-layered structure consisting of an inner core cylinder and a surrounding outer annular cylinder. This slow waveguide works as an end-fire radiator when operated with a point source attached on its end. In this paper, a theoretical study on propagation of sound waves along the composite slow waveguide is performed. The phase velocity, cutoff wave number, sound pressure distribution and acoustic power are obtained in dependence on parameters pertaining to the composite system. A new propagation phenomenon which is not obtainable in usual single-structured slow waveguides is described. The limiting case of the composite slow waveguide-a thin-layered composite slow waveguide-is also discussed.

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The characteristics of structure-borne sound propagation through the various types of junctions without or with blocking-masses like beams and columns are studied numerically when the bending wave or the longitudinal wave is normally incident on the junctions. The following facts are found. In the case of one typical building structures made of dense concrete, almost all the energies of bending and longitudinal waves are reflected at the junction by the blocking-masses above 1000Hz, and the effects of blocking-masses are little below 50Hz. In the case of the bending wave incidence, much energy transmits through the junction at a frequency peculiar to the junction because of the existence of the blocking-mass. When the longitudinal wave is incident on, the characteristics of propagation greatly depend on whether the structure, i. e., a plate, is or not on the extension line of the plate on which the wave is incident. In the case of junctions intersected at an arbitrary angle, it is found that the wave of different type from the incident one is generated gradually with increase of the turning angle.

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If the first reflection from a rigid curved surface hits other panels, or the inside of a concave panel has other specular reflection points, discrete reflections among these multiple reflections change their transfer functions very much. It is already shown that multiple reflections of a geometrical wave and boundary waves are separately calculated between rigid plane panels. An impulse response from a rigid curved panel resembles that of a rigid plane panel. A discrete reflection around the specular reflection point of the first panel is replaced by an equivalent image point source and the second reflection between rigid curved panels is estimated by the first reflection of it. The multiple reflections inside a rigid concave panel with large curvature and the contribution of wide area around the specular reflection point can be also approximately calculated by the equivalent image point source from the strength of the first reflection. These calculated results are compared with measured ones in the time and frequency domains.

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A method is presented of describing numerically the three dimensional shape of human head. By making use of the method the statistics on the head shape are obtained in 52 male young adult Japanese. Contours of the head are drawn by an apparatus whose principle of operation is similar to that of the perigraph used in the craniometry. After the contours and the positions of reference points are processed by a digital computer, the head shape is represented in the spherical coordinate system UA (R, Θ, Ø) as well as the rectangular Cartesian coordinate system U (X, Y, Z) where the origin is at the midpoint of the right-and-left tragions, X-axis is passing through the tragions, Y-axis is on the Frankfort horizontal, and Z-axis is perpendicular to both X-axis and Y-axis. The statistics on the radius R in the direction with polar angle Θ and azimuth Ø at intervals of six degrees are obtained: the average, standard deviation, maximum, and minimum are shown. Finally, a method of generating a model head which may be used in the dummyhead-headphone system is described. The shape of the model head is based on the statistical values obtained.

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