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Adding a wave to its own mirror

Why Does Noise-Cancelling Work?

Noise-cancelling headphones play the exact opposite of the noise, and the two add up to quiet.

The noise arriving A pattern of pressureWhat the headphone adds The exact oppositepattern
Add a wave to its own mirror image and you get silence.
  1. Step 1 of 5

    Two waves can cancel each other out.

    1 A wave pushingoutward2 A wave pullingin at the sameinstant3Together theyadd up tonothing

    Where one wave squashes the air and another stretches it by the same amount at the same instant, the air simply does not move at all.

  2. Step 2 of 5

    The headphone listens before it plays.

    A microphone on theoutsideA chip that flips thesignalThe speaker inside thecupA second mic checkingthe result

    A microphone on the outside of the cup samples whatever noise is arriving, so the chip knows exactly what shape it has to cancel.

  3. Step 3 of 5

    Flipping the wave has to be fast.

    Hear the noise Invert it Play the opposite Thousands oftimes asecondLoop

    The opposite wave is only useful if it arrives at the same moment as the noise, so the whole measure-flip-play loop has to run continuously.

  4. Step 4 of 5

    Steady low rumble is the easy case.

    Engine drone — 100 Hzalmost erasedVoices — 1,000 Hzpartly reducedCutlery — 5,000 Hzbarely touched

    An engine drone repeats predictably, so the next wobble is easy to anticipate. Clattering cutlery is different every time and mostly gets through.

  5. Step 5 of 5

    High notes are too short to catch in time.

    A slow wave — easy toanticipate A fast wave — gone toosoon

    A fast wave has finished before the chip has measured it, so by the time the opposite is played the original has already moved on.

    A 1,000 hertz wave repeats every millisecond, so the chip has well under that to measure it, flip it and play the opposite.

The short version

Noise-cancelling headphones record the noise and play its exact opposite, so the two waves add together into something much quieter.

Try it yourself

Wear noise-cancelling headphones with nothing playing, first on a bus and then in a busy café. The engine rumble goes; the chatter does not.

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