What happens to the energy during destructive interference?

Question

When two waves of the same magnitude and same wavelenght collide in opposite phase, destructive interference occurs and it makes a flat wave with 0 amplitude therefore 0 energy. But where does this energy go? And how does it come back so that both waves can continue going?

Answer 1

In the case of acoustic energy, imagine two woofers attached face-to-face and being driven out of phase. The net result is that they push the same parcel of air back and forth with no radiated energy. If they are tightly coupled, both mechanically to each other and electromagnetically to their amplifiers, their impedance will be high and they will draw negligible power. (This ignores the sound radiated at their rear surfaces; they will actually function as one speaker.)
Things tend to seem paradoxical when it comes to electromagnetic energy. It's because we're dealing with beamed energy. The beam splitter example seems logical, but suppose there is no beam splitter, just two beams traveling along the same path? Well, to get perfect destructive interference, you'd have to have both sources lying on the same line to the target. (If they're angularly separated, you get the familiar pattern of alternating constructive and destructive interference). But the nearer source would have to be transparent as well as being an out-of-phase emitter, so the net output from the nearer source would be zero. This is equivalent to its simply absorbing the energy from the farther one, so that energy would heat it. Or the two sources would have to occupy the same point (each absorbing the other's energy) which sounds like a "forbidden" condition. I'd check the reference for a better explanation.

Answer 2

When such interference takes place in a lossless manner (where the waves are not thermalized), the setup invariably involves another route for the energy to be diverted too. For example, combining two waves with amplitudes A and B using a beamspitter results in A + B when A is reflected and B is transmitted if the other branch where A is transmitted and B is reflected results in A - B

Answer 3

The waves do not have opposite phase everywhere. In some places they are in phase, and we have constructive interference. That is where the energy is.