Question

‧How do you reconcile the principle of conservation of energy with the observation that, in one region, the wave medium is not in motion when waves interfere destructively?

Answer 1

If the waves are cancelled everywhere, that would violate energy conservation law. Actually what happens is that there is a redistribution of energy. There are regions where there is constructive interference and there is exactly the equal amount of extra energy that is being shifted from another region having destructive interference and thus the total energy over all space is conserved. (same case also happens when there is an energy flow, energy flows from one region to another but the total energy is conserved.