On the Vibration of a Sphere Caused by Plane Progressive Sound Waves

Abstract

When a rigid movable sphere is put into the sound field, the sound pressure acts on this sphere and causes it to vibrate. In this case the velocity of vibration is proportional to the magnitude of incident sound pressure. Applying this principle, we can develop a spherical velocity-microphone. But its velocity depends upon the product of radius of the sphere and frequency of incident sound waves, and also upon the ratio of densities of sphere and medium. Therefore, in designing these microphones it is necessary to estimate the magnitude and frequency character of its velocities, i. e. , frequency response of its sensitivities. In this paper, we have estimated these values from the solutions of the wave equation which satisfy the boundary conditions of vibration. And then we obtained the relation among the vibromotive force acting on the fixed obstacle, the radiation impedance presented by the vibrating obstacle, the mass of the obstacle, and the velocity of the vibrating obstacle. This relation can be applied to estimate the velocity of any movable sphere from the vibromotive force, the radiation impedance and the mass for its sphere, and these results were found to coincide with above calculation.