ASA 128th Meeting - Austin, Texas - 1994 Nov 28 .. Dec 02

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.