Interaction between a CW plane wave and a rectangular plane pulse

The interaction between a plane CW and a plane pulse travelling at the velocity of sound is considered. Both the CW and pulse satisfy the homogeneous wave equation and are used to study the scattering of sound waves by sound outside their common region of interaction. It is shown that there is no scattering outside the region of interaction, which follows the law of causality. It is also shown that it appears to be inappropriate in this particular case to apply Lighthill's far field integral for calculating the scattering of sound by sound.