system
Given the following post, respond as if you're commenting on Reddit:
human
Where does "sound energy" goes, in active noise cancelling headphones ?

My understanding of noise cancelling headphones is that the headphone will produce the opposite of the external sound, and when added, those two sounds will cancel each other. This will result in no sound.

The headphone uses energy to produce his sound wave. The external sound wave has an energy. 
The resulting soundwave (which is the sum of the two others) has no energy since its amplitude is 0.

So, where do the initial energy of the soundwave and the energy of the headphone-produced soundwave go ?
gpt
There can never be total destructive interference throughout all space if the source of the two waves are not spatially identical.

In other words, there will be destructive interference in a specific area, but there will be a corresponding constructive interference elsewhere such that total energy is still conserved.