Peter J. Westervelt
Dept. of Phys., Brown Univ., Box 1843, Providence, RI 02906
Two arbitrary pulses p[sub 2](t-c[sub 0][sup -1]x) and p[sub 1](t+c[sub
0][sup -1]x) each of width c[sub 0](tau) pass through one another at x=0,
generating a differential surface mass rate source density d(sigma)[sub
s](t,x)=q[sub s] dx where q[sub s]=Ad(p[sub 1]p[sub 2])/dt and A= ((rho)[inf
0]c[inf 0][sup 4])[sup -1][2 + (rho)[inf 0]c[inf 0][sup -2](d[sup
2]p/d(rho)[sup 2])[inf (rho)[inf 0]]]. The equation for the scattered pressure
p[sub s] is d[sup 2]p[sub s]/dx[sup 2]-c[sub 0][sup -2] d[sup 2]p[sub s]/dt[sup
2]=-q[sub s] and its solution is p[sub s](x',t)=(integral)dp[sub s]=(c[sub
0]/2)(integral)d(sigma)[sub s]=(c[sub 0]/2)(integral)q[sub s](x,t')dx, t' being
the retarded time; thus, (p[inf s])[inf (plus or minus)] = (c[inf
0]/2)A(integral)[inf (plus or minus)c[inf 0](tau)/2][sup x'][d(p[inf 1]p[inf
2])[inf t=t'(plus or minus)]/dt]dx, where + is chosen when x'