At the left, two normal waves (bottom) and their combined waveform (top). At the right, the two bottom waves are mirror images of each other, and the combined waveform on top is null, or silent.
Great post from Kirk McElhearn ... Three-Minute Tech: How noise-canceling headphones work
The technology works using tiny microphones on the outside of the headphones that monitor ambient sounds, along with special circuitry inside the headphones that turns those sound waves upside down and feeds the resulting inverted waves through the headphones to your ears. This results in destructive interference—when you take two sound waves that are out of phase (each a mirror image of the other), they cancel each other out, resulting in silence. In other words, that external noise is, well, canceled.
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