| Popis: |
Starting with Eckart’s equation for ρs the scattered density [P. J. Westervelt, J. Acoust. Soc. Am. 29, 934 (1957)], ⧠2ρsc20=⧠2E12 −∇2(2T12+ΛV12), the variables x0=c0t and ψ,0=−(4ρ0c20)−1/2p are introduced for which ⧠2ψ=0, ⧠2ψ2=T12−V12, and ∇2V12=⧠2V12+(V12),00 to obtain ⧠2[ρsc20+T12+(Λ−1)V12 +2(ψ2),00]=−2(2+Λ)[(ψ,0)2],00. Next it is assumed that ψ=φ+χ, where φ(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 φ and χ are retained; thus (ψ,0)2=2χ,0φ,0, and since ∇φ=−nφ,0, it is found ⧠2(σφ)=2∇σ⋅∇φ−2σ,0φ,0=−2φ,0 χ,0, leading to the solution of Eckart’s equation, ρsc20=(2−Λ)V12−E12 +2[(2+Λ)σφ−ψ2],00, valid within the interaction zone, but vanishing outside where V12=E12=σ=φ=ψ=0. The feasibility of making optical measurements of ρs is being investigated. |
