How do noise-cancelling headphones work?

Noise-cancelling headphones listen to the sound around you through small microphones, then play a copy of it flipped upside down through the speakers. Where the two waves meet near your eardrum, each push of air is met by an equal pull, and they largely cancel. This works best on steady, low-pitched noise like an engine's drone. Faster, higher sounds, including voices, are left mostly to the seal of the ear cushions.

What is anti-noise?

Sound is a wave of tiny pressure changes, little squeezes and stretches of the air arriving one after another. If you add a second wave that stretches wherever the first squeezes, the two sum to almost nothing. The acoustics consultancy Acentech describes the anti-noise as the inverse of the sound pressure waveform you want to cancel. For it to work, the amplitude and frequency have to match and the phase has to be opposite.

The idea is old. Paul Lueg's US patent, "Process of silencing sound oscillations", was filed in 1934 and granted in 1936. It describes a microphone feeding an amplifier and a loudspeaker, arranged so that, in Lueg's words, "each time when a thickening of the air meets the microphone the loudspeaker answers by a corresponding thinning of the air". Nearly a century later, the principle in your headphones is the same. The electronics are what changed.

Picture two people pushing on a revolving door from opposite sides with exactly the same force at exactly the same moments. The door barely moves. If one of them is a fraction late, or pushes harder, it twitches. Noise cancelling depends on timing in the same way.

Why does it work best on low, steady sounds?

The first reason is wavelength. NASA's Glenn Research Center gives the speed of sound at sea level as roughly 1,100 feet per second. Divide that by the frequency and you get the length of one wave. A 100 hertz hum is about 11 feet long, a bit over three metres. A 1,000 hertz tone is about a foot. The space inside an ear cup is tiny compared with a low-frequency wave, so the pressure is nearly the same everywhere inside it. Cancel it at the microphone and you have cancelled it at your eardrum too. Acentech puts the practical limit at around 1,000 to 2,000 hertz. Above that, the waves get short enough that the sound field in the cup is no longer uniform, and cancelling at one spot no longer means cancelling at another.

The second is delay. The system has to hear the noise, compute the inverse and play it before the moment has passed. The Helmut Schmidt University overview of these designs notes that the attenuation bandwidth of the in-cup feedback approach is limited by delays in the control loop. A slow wave forgives a small delay. A fast one doesn't.

Set delay error to zero, then add a little and switch between slow and fast waves. Press Play to follow the pressure changes at the ear over time.

Steadiness matters for the same reason. A fan or an engine produces the same pattern over and over, so the electronics can lock on to it. Acentech notes that rapidly changing sounds such as speech are harder to cancel. A 2021 survey of noise-control techniques calls impulsive noise, rare but large bursts, a great challenge for cancellation systems. That survey also mentions the waterbed effect in feedback systems, which means it is theoretically impossible to suppress noise at all frequencies at once.

Feedforward, feedback and hybrid

Headphones put their microphones in one of two places, or both.

Feedforward uses a microphone on the outside of the ear cup. It hears the noise slightly before it reaches your ear, and that head start lets the system cancel sounds up to higher frequencies than a feedback system could, according to Acentech. The catch is that it is guessing what will arrive inside the cup. It can only cancel the part of the noise that matches what the outside microphone heard, it is vulnerable to wind, and it can't tell when the headphones sit differently on your head.

Feedback uses a microphone inside the cup to measure what is actually left at your ear and correct it. It adapts to fit, but its delay has to stay very short. The survey notes that many headphones handle this loop with analogue circuitry, which is cheap, easy on batteries and fast.

Hybrid designs combine the two. The Helmut Schmidt University paper describes hybrid structures as a way to partially compensate for the limits of each, at the cost of more complexity.

What do the ear cushions do?

Blocking sound with a physical seal is called passive isolation, and it is strongest roughly where active cancellation is weakest. Acentech notes that passive attenuation tends to be more effective at higher frequencies than at low ones. The 2021 survey makes the mirror point that passive methods, such as sealing and shielding, struggle with low-frequency noise and get bulky when they try.

So a pair of noise-cancelling headphones is really two systems with a handover. The electronics handle the low rumble. The foam and the seal handle the hiss and the chatter. A loose fit hurts both. Sound leaks past the seal, and a feedforward system can't tell that the fit has changed.

Noise cancelling doesn't block every sound

It doesn't, and it was never designed to. The cancellation targets the low, continuous part of the noise around you. A colleague talking or a dropped plate still gets through, softened mainly by the cushions. When headphones seem to make voices disappear, most of the credit belongs to a good passive seal.

Cancellation is also local. Acentech points out that making a wave vanish at one point does not guarantee it vanishes anywhere else. That is why the trick is far more practical in a small, sealed ear cup than in an open room.

Faster chips, quieter rooms

Two questions follow naturally: how the chip works out the anti-noise fast enough to keep up, and how earplugs manage the high frequencies with no electronics at all. Ask Learnfold and it sketches a course for you to approve, then branches a new page off each question you follow, the way a curiosity rabbit hole does. Adding waves also explains why one note sounds different on a piano and a guitar. The pages are AI-written, so check the important parts against a reliable source.