Pulses pass through each other unchanged
While two pulses overlap their displacements add, but afterwards each pulse carries on with its original shape, amplitude, speed and direction. At the instant two equal and opposite pulses fully cancel, the medium is momentarily flat but the particles are still moving, so the energy is entirely kinetic and nothing has been destroyed.
What this actually means
Waves are not billiard balls. They do not bounce off each other or lose anything in the collision. The overlap is temporary bookkeeping; each pulse is unaffected once it has passed.
The flat moment scares students because it looks like energy vanished. It has not. At that instant every particle is at zero displacement but moving at maximum speed, so the whole energy is kinetic. A frame later the pulses reappear.
This is exactly why the fully destructive point of an interference pattern is not a violation of conservation of energy. Energy is redistributed from the minima into the maxima, not removed.
A favourite exam sketch is two pulses of the same shape but opposite sign meeting head on. Draw three frames: before, at full overlap (a flat line), and after (both pulses restored, still travelling apart).
If the pulses have different shapes, the overlap frame is just the point-by-point sum, which usually looks lumpy and asymmetric. That is fine. It does not need to be a neat shape.
Saying the pulses are destroyed or cancel permanently, instead of saying they cancel only at that instant and then pass through unchanged.
Prove it — watch it be true
- Choose the two-pulse mode and set the second pulse to be inverted.
- Step frame by frame to the full-cancellation instant and confirm the resultant trace is flat.
- Continue stepping and confirm both pulses re-emerge with their original height and width.