Two arbitrary pulses p2(t−c−10x) and p1(t+c−10x) each of width c0τ pass through one another at x=0, generating a differential surface mass rate source density dσs(t,x)=qs dx where qs=Ad(p1p2)/dt and A= (ρ0c40)−1[2 + ρ0c0−2(d2p/dρ2)ρ0]. The equation for the scattered pressure ps is d2ps/dx2−c−20 d2ps/dt2= −q̇s and its solution is ps(x’,t)=∫dps=(c0/2)∫dσs= (c0/2)∫qs(x,t’)dx, t’ being the retarded time; thus, (ps)± = (c0/2)A∫±c0τ/2x’[d(p1p2) t=t’±/dt]dx, where + is chosen when x’<x, − when x’≳x, and t±’ = t ± c0−1(x’− x). Suppose x’≳c0τ/2 then x’ lies outside the interaction zone, it is found that (ps)−= (c20A/4)(p2p1+ṗ2∫t−∞p1dt)=0 unless p1 has a nonzero average which is possible for plane waves but it is assumed that this is not the case [L. D. Landau and E. M. Lifshitz, FluidMechanics (Addison-Wesley, Reading, MA, 1959), p. 267]. In the event x’<−c0τ/2x’ again lies outside the interaction zone and (ps)+= (c20A/4)(p1p2+ṗ1∫t−∞p2 dt)= 0. Within the interaction region −c20/2<x’<c0τ/2 so that ps=(ps)+ +(ps)−=(c20A/4)(2p1p2 +ṗ2∫t−∞p1 dt+ṗ1∫t−∞p2 dt), which is precisely the result obtained previously [P. J. Westervelt, J. Acoust. Soc. Am. 94, 1774 (A) (1993)], recalling that p1 is here a plane wave; thus in the earlier result pm=p1/2. The zero scattering results obtained here conflict with nonzero results obtained by Trivett and Rogers [J. Acoust. Soc. Am. 71, 1114 (1982)] in a related problem, which most likely stems from spurious sources arising from discontinuities similar to those that plagued Ingard and Pridmore-Brown.