This is related to this question on Aviation.SE about noise cancelling headsets.
We know that soundwaves can be superimposed on each other. Therefore, by taking an existing sound wave and producing a second wave which is exactly its inverse, the two will sum up to zero. This is how active noise cancelling headset works - by "listening" to the exterior sound with a microphone, then reverting it in its speaker.
The problem is, where does the energy go? The noise sound is an energy source. Generating an inverted sound on the drums of the speaker is also an energy source (from the electricity which powers the speaker). So the total energy output cannot be zero. But we hear silence! Where does that energy go?
EDIT: I'm more interested in a theoretical answer, assuming a perfect world with no energy loss in converters / out-of-sync waves. Although an answer giving real world converter efficiencies is also useful.