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From The Science of Everyday Life

Noise-cancelling headphones work by generating a sound wave that is:

  1. Much higher in pitch so the ear ignores the original
  2. Inverted in phase relative to the incoming noise
  3. Louder than the noise, masking it completely
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Answer: Inverted in phase relative to the incoming noise

A microphone samples the ambient sound and the headphone emits a wave whose peaks line up with the noise's troughs, so the two largely cancel. It works best on steady low-frequency sound like engine drone.

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