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