system
Given the following post, respond as if you're commenting on Reddit:
human
When two waves destructively interfere, where does the energy go?
gpt
Destructive interference occurs either at some moment of time or at some point in space.  In time, if two waves meet each other and 
destructively interfere, then a few moments later they will have traveled some additional distance and will constructively interfere.  In space, if two waves produce a dark spot at some point then there will be a bright spot at a different point.  The energy canceled out by destructive interference is always compensated by the energy doubled up from constructive interference.

EDIT:  There seems to be some confusion as to how this works.  The superposition cos(kx + vt) + cos(kx + vt + pi) = 0 represents two waves propagating in the same direction which cancel everywhere, which is a trivial solution to the wave equation. It means nothing was emitted in the first place.  If you reverse the propagation direction of one of them, they will not cancel everywhere.  This is what is meant by interference.  

EDIT 2:  The reason this probably seems surprising is because wave interference is usually taught by considering only the spatial variables for simplicity.  Using only spatial dependence means you have selected one particular moment in time.  But apart from the trivial solution discussed above, *total destructive interference cannot occur at all positions at all times*.  And this is the whole point of the question.  If waves could simply disappear, energy would not be conserved.  

EDIT 3:  sin(kx - vt) + sin(kx + vt + c) = 2sin(kx + c/2)cos(vt + c/2), where c is the phase shift.