eli5: How do noise cancelling headphones work with the flick of a switch?

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eli5: How do noise cancelling headphones work with the flick of a switch?

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[Destructive Interference](https://en.wikipedia.org/wiki/Wave_interference). Sound waves are pressure waves in a medium. As waves obey the [superposition principle](https://en.wikipedia.org/wiki/Superposition_principle) – that is, the amplitudes of waves add arithmetically – we can create a second wave with opposing amplitudes, thereby canceling out the original wave.

Noise canceling headphones have microphones that measure incoming sound waves and create artificial sound waves canceling out the the incoming waves in the area around your ear.

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