Radiation Pressure on a Small Rigid Sphere

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 Ta and Va 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∇Ta − ∇Va]+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 ∇Ta and ∇Va, 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.