The reflection of a Gaussian pulse of a plane ultrasonic wave from rigid and elastic spheres in water

Abstract

The authors have determined shapes and amplitudes of Gaussian pulses with limit frequencies equal to 2. 3. 10 and 20 kHz which were reflected backwards from rigid and steel spheres with a 0.5 m radius, immersed in water. For this purpose spectral analysis, transmittance theorem and inverse Fourier transform were used. Reflected pulses exhibited two maxima corresponding to a specular reflection from the face surface of the sphere and to a creeping travelling wave around the sphere. These maxima were masked by many resonances inside of the elastic sphere. The masking effect decreases with the decrease of the limit frequency of the Gaussian pulse incident upon the sphere. In such a case the shape of the reflected pulse tends to a time derivative of the incident pulse. The peak to peak pressure of the reflected pulse remains unchanged in the range of limit frequencies under investigation. The measurement of the time interval between the first and second maximum of the reflected pulse makes it possible to determine the radius of the elastic sphere, if the limit frequency is sufficiently low.