## 4pPAa2. Scattering of sound by sound within the interaction zone.

Peter J. Westervelt

Dept. of Phys., Brown Univ., Box 1843, Providence, RI 02912

Starting with Eckart's equation for (rho)[sub s] the scattered density [P. J. Westervelt, J. Acoust. Soc. Am. 29, 934 (1957)], (open square)[sup 2](rho)[sub s]c[sub 0][sup 2]=(open square)[sup 2]E[sub 12] -(del)[sup 2](2T[sub 12]+(Lambda)V[sub 12]), we introduce the variables x[sup 0]=c[sub 0]t and (psi)[sub ,0]=-(4(rho)[sub 0]c[sub 0][sup 2])[sup -1/2]p for which (open square)[sup 2](psi)=0, (open square)[sup 2](psi)[sup 2]=T[sub 12]-V[sub 12], and (del)[sup 2]V[sub 12]=(open square)[sup 2]V[sub 12]+(V[sub 12])[sub ,00] to obtain (open square)[sup 2][(rho)[sub s]c[sub 0][sup 2]+T[sub 12]+((Lambda)-1)V[sub 12] +2((psi)[sup 2])[sub ,00]]=-2(2+(Lambda))[((psi)[sub ,0])[sup 2]][sub ,00]. Next we assume (psi)=(phi)+(chi), where (phi)(x[sup 0]-n(centered dot)r) is a plane wave and (chi)[sub ,0]=(sigma)[sub ,0]+n(centered dot)(cursive beta)(sigma), where (sigma)(x[sup 0],r) is an arbitrary wave. We retain terms bilinear in (phi) and (chi); thus ((psi)[sub ,0])[sup 2]=2(chi)[sub ,0](phi)[sub ,0], and since (cursive beta)(phi)=-n(phi)[sub ,0], we find (open square)[sup 2]((sigma)(phi))=2(cursive beta)(sigma)(centered dot)(cursive beta)(phi)-2(sigma)[sub ,0](phi)[sub ,0]=-2(phi)[sub ,0](chi)[sub ,0], leading to the solution of Eckart's equation, (rho)[sub s]c[sub 0][sup 2]=(2-(Lambda))V[sub 12]-E[sub 12] +2[(2+(Lambda))(sigma)(phi)-(psi)[sup 2]][sub ,00], valid within the interaction zone, but vanishing outside where V[sub 12]=E[sub 12]=(sigma)=(phi)=(psi)=0. The feasibility of making optical measurements of (rho)[sub s] is being investigated.