Eli5: How does active noise cancelling work on headphones?
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Sound is waves. Active noise cancelling creates an inverted form of the incoming sound wave. When the waves overlap they cancel each other out.
Waves have an intuitive property where if two overlap (called inteference), the wave can be modelled as simply the addition of the two. You know [how a soundwave looks?](https://www-users.cse.umn.edu/~rogness/math1155/soundwaves/a.png).
When two waves interfere, you usually get some **Constructive Interference** (parts adding to get bigger) and **Destructive Interference** (two parts adding to get closer to the 0 line in the middle). The former makes things louder, the latter makes them quieter.
Now, given that, what if we had two waves that were exactly opposite one another? All the points above the middle on one are the same distance below on the other? Then they’d all add to zero!
That’s the idea behind Active Noise Cancelling. Make a wave that cancels the noise from outside the headphone so that they interference when you’re going to hear them. Usually this is done with some small microphones on the outside of the headphone, picking up the sound and then a microcontroller inverting it.
Sound moves in waves.
Say “Sound X” is what you’re trying to cancel.
Sound waves have two important characteristics when it comes to this: the amplitude and the phase.
(There’s more that goes into this, but think the “strength” and the “timing” of a given sound wave, respectively)
If you get “Sound Y” that has the same amplitude but opposite phase of “Sound X”, Sound Y will interfere with Sound X to form a new wave altogether, and effectively cancel both Sound Y and Sound X out.
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