If you hear two sound waves hit the same air, they add their waves together.
If you had two identical waves and they were in sync (both go “up” and “down” across the line at the same times) then playing them at the same time would make it sound like the same thing but twice as loud.
But if the second wave was exactly like the first wave *except* it was mirrored (it goes down when the other goes up), then adding them together would mean the second *subtracts* from the first and instead of sounding twice as loud it would just subtract to zero and be silent.
A noise cancelling headphone is designed to do that. It has a microphone that listens to the sound wave in the outside air that’s about to hit your ear, then it plays an inverted version of that same sound wave in its speakers, but at a lesser volume so it doesn’t completely null out the sound, but just subtracts *some* volume from it.
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