Scattering of sound by sound within the interaction zone.

Starting with Eckart's equation for ρs the scattered density [P. J. Westervelt, J. Acoust. Soc. Am. 29, 934 (1957)], [Laplacian_variant]2ρsc20=[Laplacian_variant]2E12 -∇2(2T12+ΛV12), the variables x0=c0t and ψ,0=-(4ρ0c20)-1/2p are introduced for which [Laplacian_variant]2ψ=0, [Laplacian_variant]2ψ2=T12-V12, and ∇2V12=[Laplacian_variant]2V12+(V12),00 to obtain [Laplacian_variant]2[ρsc20+T12+(Λ-1)V12 +2(ψ2),00]=-2(2+Λ)[(ψ,0)2],00. Next it is assumed that ψ=[lowercase_phi_synonym]+χ, where [lowercase_phi_synonym](x0-n·r) is a plane wave and χ,0=σ,0+n·∇σ, where σ(x0,r) is an arbitrary wave. Terms bilinear in [lowercase_phi_synonym] and χ are retained; thus (ψ,0)2=2χ,0[lowercase_phi_synonym],0, and since ∇[lowercase_phi_synonym]=-n[lowercase_phi_synonym],0, it is found [Laplacian_variant]2(σ[lowercase_phi_synonym])=2∇σ·∇[lowercase_phi_synonym]-2σ,0[lowercase_phi_synonym],0=-2[lowercase_phi_synonym],0 χ,0, leading to the solution of Eckart's equation, ρsc20=(2-Λ)V12-E12 +2[(2+Λ)σ[lowercase_phi_synonym]-ψ2],00, valid within the interaction zone, but vanishing outside where V12=E12=σ=[lowercase_phi_synonym]=ψ=0. The feasibility of making optical measurements of ρs is being investigated. [ABSTRACT FROM AUTHOR]