Radiation Force on Bodies in a Sound Field

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Abstract
A simple derivation of the force which acts on a body placed in sound field is given. The tensor properties of the force are exhibited, but it is also shown that for a rigid body the force may be derived from the scalar pressure alone. It is shown how the time average force is determined by the momentum lost by the sound wave during the collision with the body. Using this result, the force is related to the scattering amplitude, and a simple expression in terms of the phase shifts is given. The connection between the force and the scattering cross section is examined. A force factor κ = K̄z/(12ρ0k2σsc) is defined. It is shown that κ = 1 for plane scatterers perpendicular incidence. A simple general formula for the force in the limit of short wavelengths is derived. It is shown that neither for very long wavelengths nor for very short ones is κ in general equal to 1. The case of a rigid sphere is treated in detail. Curves are shown for the force and for the force factor κ.

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