Frequency dependence of the acoustic radiation pressure on a solid sphere in water

Abstract

The frequency dependence of the acoustic radiation pressure on a solid elastic sphere placed freely in an incident plane progressive sound field in water has been investigated. In particular, the behavior of the acoustic radiation pressure at resonance frequencies of the elastic vibration of the sphere has been studied theoretically by taking into account the three components of the radiation pressure, namely, kinetic energy, potential energy, and tensor term. It has shown that the contribution of potential energy to radiation pressure is the largest and it has a positive value, that which of kinetic energy is rather small and has a negative value, and that which of tensor term is so small as to be negligible in the cases far from resonance frequencies. At resonance frequencies, potential energy falls off rapidly, while the softer the material are, the greater positive values kinetic energy and tensor term are increased up to, with a few exceptions. As a result, there takes place, in general, a series of maxima in the frequency characteristic curves of radiation pressure for relatively soft materials such as lead, and a series of minima for relatively hard materials such as iron at the resonance frequencies, because the increase in kinetic energy and in tensor term overcome the decrease in the potential energy for relatively soft materials. Materials of intermediate hardness such as brass have the frequency characteristic curves mixed by maxima and minima.