Simple expressions are derived for the acoustic radiation force F on a small rigid sphere of radius a, volume v and density ρ suspended In a liquid or gas of density ρ0. Effects of viscosity are neglected; use is made of methods developed by King and Embleton. Results are expressed in terms of the time-averaged densities T̄a and V̄a of kinetic and potential energies, respectively, in the incident sound field. Letting β be ρ0/ρ it is found. as an approximation when a is much less than the sonic wavelength, that F = v[B∇T̄a − ∇V̄a]+Δ, B − 3 1 − β /(2+β), where Δ is given by a relatively complicated expression. The quantity Δ is important primarily in progressive waves of relatively uniform amplitude, as exist in the field of a large source; here ∇T̄a and ∇V̄a, may be relatively small while gradients of the phase exist. In a standing wave or in the neighborhood of a small source, Δ is negligible. When Δ = 0, the above expression for F agrees with one given previously by Gor'kov.
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Wesley L. Nyborg (1967) studied this question.