A theoretical examination is made of the scattering cross section of an obstacle plunged into plane incident waves, concerning their limiting wave lengths. The scattering cross section, which is proportional to the imaginary part of amplitude of the scattered wave in the forward direction, is formulated in a form that is stationary with respect to small variations of the surface fields. These fields are dominated by amplitude functions both at the high and the low frequency ranges. The Rayleigh's scattering law for long wavelength is set forth as well, as twice the geometrical cross section, in the limit of short wavelength.
A series of analysis for the zonal sound radiator has been performed. As the last part of these research, the analysis for the zonal vibration of an oblate spheroid has been developed in this paper. The directivity of radiated sound pressure and power, and the radiation impedance have been calculated. Four previous results, i. e. the data on cylinder, prolate spheroid, sphere, and oblate spheroid, were compared with each other. These data may be usefull for the design of the wide frequency range mushroom sound radiator.
The application of the phase method in visualizing ultrasonic waves by the secondary interference method are theoretically described. The visibility of the image of the waves can be always increased by the method. The amplitude condition and the phase condition of the phase plates required in obtaining the maximum visibility of the image are given in case of the visualization of the phase grating, the progressvie ultrasonic wave, and the stationary ultrasonic wave respectively. The results obtained can be also applied to the theory of the image formation in the phase microscopy.
Following the previous paper, the amplitude and phase conditions for obtaining the maximum visibility of the secondary interference image of progressive ultrasonic waves illuminated stroboscopically by the phase method are theoretically obtained and the results are graphically plotted against the observed positions for various intensities of the waves. Next, the principle of the phase method in visualizing ultrasonic waves are explained by the vector method.
The theoretical image curves of the Fresnel diffraction patterns caused by superposed ultrasonic waves for various sound intensities and for various observing positions are obtained from our theory developed in the previous paper. The curves are compared with the experimental results obtained by using superposed ultrasonic waves(frequencies two megacycles)crossing perpendicular to each other, showing a fair agreement between them. The changes of the visibilities of the images with the observing positions and the intensities of the waves are discussed in detail.