The energy is literally going into each wave and scattering them.
Imagine a child on a swing with a parent behind them pushing them. As long as the parent pushes while the child is starting to move forward, they are performing constructive interference and the child will go higher and higher. But if they push while the child is coming towards them that creates destructive interference that slows the swinging. And when that happens the extra energy is channeled into the body of the child and the arms of the parent. This could even potentially injure one or both of them if enough force is involved.
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