How do noise-cancelling headphones work?

The principle

Step 1: Sound is a pressure wave. A speaker cone pushes the air in front of it, then pulls back. The air molecules get squeezed together, then spread apart, over and over, and each layer passes the push on to the next. That travelling pattern of high and low pressure is sound. It moves at about 343 metres a second in air.

Step 2: Frequency and amplitude. Frequency is how many squeezes pass each second, measured in hertz (Hz): a few hundred for a deep hum, thousands for a hiss. Amplitude is how big the squeeze is, which you hear as loudness.

Step 3: Microphone and speaker. A microphone is a thin skin that the wave wiggles; the wiggle is turned into an electric signal, an electric copy of the wave. A speaker does the opposite: the electric signal moves its cone, and the cone makes the wave again.

Step 4: Adding waves together. When two waves meet in the same place their pressures add up. Two matching waves make it louder. But take the mirror image (high pressure where the noise has low, and low where it has high) and every squeeze lands in a gap. They cancel out: anti-noise.

Step 5: It has to be on time. The mirror wave only cancels if it arrives in step. One wave of a 100 Hz engine drone lasts 10 milliseconds, so a tiny delay barely matters. One wave of a 2000 Hz voice sound lasts only half a millisecond, and the same delay leaves much of it uncancelled. That’s why active cancelling works best on low, steady sounds below about 1000 Hz.

Step 6: Two microphones. A feedforward microphone on the outside of the earcup hears the noise before it reaches your ear, giving the chip a head start. A feedback microphone inside the earcup listens to what actually got through and corrects what’s left. Most good headphones use both (called hybrid). The chip turns the signal into its mirror image and plays it through the same speaker as your music.

Step 7: Passive or active?

• Passive (cushions and closed cups, earplugs): Upside: no battery, and it is good at blocking higher sounds like voices and hiss. Downside: deep drone passes straight through.
• Active (noise cancelling): Upside: it removes the deep drone of planes, trains and engines. Downside: it needs a battery and the electronics, and it helps much less with voices and sudden sounds; some people feel a slight pressure. Real headphones combine both.

Try it yourself: with noise cancelling on, hum a deep note, then whistle. The hum from outside shrinks far more than the whistle.