ASA 126th Meeting Denver 1993 October 4-8

2aPAb3. Nonscattering of sound by sound: Exact second-order transient solutions.

Peter J. Westervelt

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

The bilinear interaction of two primary waves p[sub 1] and p[sub 2] generates a scattered wave p[sub s] satisfying (open square)[sup 2]p[sub s]=-q[sub s]=-A(p[sub 1]p[sub 2]+p[sub 1]p[sub 2]), where A=((rho)[sub 0]c[sub 0][sup 4])[sup -1][2+(rho)[sub 0]c[sub 0][sup -2](d[sup 2]p/d(rho)[sup 2])[sub (rho)[sub 0]]]. Here, p[sub 1]=p[sub d]+p[sub m] was chosen in which p[sub d]=-(cursive beta)(centered dot)[(4(pi)r)[sup -1](iota)G(t-c[sub 0][sup -1]r)] and p[sub m]=-(4(pi)c[sub 0]r)[sup -1]G(t-c[sub 0][sup -1]r). This combination of dipole and monopole sources located at r=0 has a far-field cardioid pattern with a null in the (iota) direction. Also chosen was p[sub 2]=c[sub 0]U((iota)(centered dot)r+r[sub 0])(sigma)[t-c[sub 0][sup -1]((iota)(centered dot)r+r[sub 0])], a plane wave originating at r=-r[sub 0](iota) and traveling in the (iota) direction. G(t) and (sigma)(t) may each have arbitrary time dependence, however, in order to avoid the bilinear interaction of primary waves with their sources, the sources were activated at t=0 and terminated at 0