How Do Noise-Cancelling Headphones Work?
written by Stefan Christoph
This is part seven of Lunch Break Physics, the series that has argued a suction cup isn’t sucking, a fridge doesn’t make cold, the sky isn’t blue because it reflects the sea, ice floats because water freezes into a roomy cage, planes fly by throwing air downward, and that the shower curtain attacks you for reasons nobody can fully pin down. This week has a clean answer again, and it’s a strange one. Standard physics below; sources at the bottom; corrections very welcome in the comments.
The story you were told
Ask how noise-cancelling headphones work and you’ll usually hear one of two things. The first is that they simply block the sound out, a better seal, thicker padding, a wall between your ear and the world. The second is cleverer-sounding and more wrong: that they detect the noise and play a louder sound over it to bury it.
Blocking is a real thing, but it’s what ordinary headphones and earplugs already do, and it’s not what the “noise-cancelling” label refers to. And playing something louder over the top is exactly backwards. If you add more sound energy to a room, the room gets louder, not quieter. Whatever these headphones are doing, it can’t be either of those, because the whole trick is that they make it quieter by adding sound. To see how that’s even possible, you have to watch two waves meet.
Watch it happen
Below, the blue wave is the outside noise and the orange wave is the anti-noise the headphones emit. The green wave underneath is the sum, the thing your ear actually hears. Start with the two waves lined up and the sum doubles, which is the “play a louder noise over it” idea and it clearly makes things worse. Now slide the phase to 180 degrees. The orange wave becomes the exact mirror of the blue one, and the green sum collapses to a flat line. Then crank the frequency and watch the cancellation fall apart.
The flat green line is the whole point. Nothing was blocked and nothing was absorbed — a second wave was added, and the total came out smaller. That only works because sound is a wave, and waves add in a way that lets a push and a pull cancel.
The actual physics
Sound is a pressure wave: the air near your ear is squeezed a little above normal, then stretched a little below, over and over [1]. Draw that as a wiggly line and the crests are the squeezes and the troughs are the stretches. Two sounds arriving at the same spot don’t fight for the space, they simply add, moment by moment. Where both push, you get a bigger push; where one pushes and the other pulls by the same amount, you get nothing. Physicists call the adding superposition, and the special case where crest lands on trough is destructive interference: two identical waves exactly out of step cancel completely, leaving zero [2].
So a noise-cancelling headphone is really a tiny, fast copying machine. A microphone on the outside samples the incoming pressure wave. The electronics flip it upside down, turning every squeeze into a stretch, and the speaker plays that inverted copy into your ear a fraction of a millisecond later. Your eardrum feels the original noise and its mirror image at the same instant, they add to nearly nothing, and the drone fades. The headphone isn’t silencing the sound. It’s answering every push with an equal pull.
Two microphones, not one
That “copying machine” is the honest cartoon, but a real headphone can’t just invert once and hope, because the noise keeps changing and no inversion is ever perfect. Good sets use two microphones and a filter that retunes itself hundreds of times a second [3].
The first is a feedforward mic on the outside of the cup. It hears the noise slightly before it works its way to your eardrum, which buys the electronics a head start against that fixed reaction delay — the more warning, the better the mirror lands. The second is a feedback mic inside the cup, sitting in the sealed pocket right next to your ear. Its whole job is to listen to what’s left over after cancellation — the residual error — and report it back so the system can nudge the anti-noise until that leftover shrinks toward zero. An adaptive filter does the nudging: it continuously adjusts the amplitude and phase of the mirror wave to drive the inside mic’s reading down, so the headphone tracks the noise as it shifts instead of assuming it stays put [3]. Sets that use both mics are called hybrid, and the inside mic is also why fit matters so much — it can only correct the sound that actually reaches the sealed cavity it lives in.
A little bit of math
Take the noise as a wave of height A and add a second wave of the same height, shifted in phase by an angle φ. There’s a clean trig identity for the sum of two equal sine waves:
A·sin(θ) + A·sin(θ + φ) = 2A·cos(φ/2)·sin(θ + φ/2)
The part that matters is the amplitude out front: 2A·cos(φ/2). That single factor tells the whole story.
- In phase,
φ = 0°:cos(0) = 1, so the amplitude is2A. Twice as tall, which for sound is about 6 decibels louder. This is the “play it louder” idea, and the math agrees it’s the wrong direction. - Exactly out of phase,
φ = 180°:cos(90°) = 0, so the amplitude is zero. Complete silence from adding a wave to a wave. - Halfway,
φ = 90°:cos(45°) ≈ 0.71, so about1.4A. Partial, messy, neither doubled nor cancelled.
Now the catch, and it’s why the frequency slider matters. Even with the adaptive filter working perfectly, the headphones can’t react instantly; there’s a small, fixed delay between hearing the noise and playing the answer. A fixed time delay is a phase error that grows with frequency, because phase error is 360° × frequency × delay. For a low 100 Hz rumble the wavelength is about 3.4 metres, and a fraction-of-a-millisecond delay is a tiny slice of that, so the mirror still lands almost perfectly and the sound cancels. For a 4,000 Hz hiss the wavelength is only about 8.6 centimetres, the same tiny delay is now a large slice of the wave, and the “mirror” arrives so far out of step that it stops cancelling and starts adding [3]. That’s the physics behind a fact every traveller knows: the engine drone vanishes, the crying baby doesn’t.
The same trick, elsewhere
Cancelling a wave with its own mirror image isn’t a headphone gimmick. It’s a general property of waves, and once you know the shape of it you see it in very different places.
- Anti-reflection coatings on glasses and camera lenses. A microscopically thin film is layered onto the lens so that light reflecting off its top surface and light reflecting off its bottom surface come back exactly out of step. The two reflections destructively interfere and cancel, which is why coated lenses look darker and let more light through. Same superposition, done with light instead of sound.
- Active silencers on car cabins and ductwork. The same microphone-and-anti-noise idea is built into some cars and into large ventilation and exhaust systems, aimed squarely at the low-frequency hum that passive baffles can’t easily stop. It’s a noise-cancelling headphone scaled up to a room.
- Dead spots between two speakers. Play the same steady tone through two speakers and walk around: at certain places the two waves arrive crest-to-trough and the sound drops away to almost nothing. Nobody engineered it; it’s the same destructive interference happening in mid-air, laid out in space instead of built into electronics.
The common thread is a wave meeting a matched, opposite wave and the two summing to less than either alone.
False friends
These all reduce noise, so they look like they belong in the same story. They don’t, because none of them work by adding an opposite wave. This is where an expert reader should look first.
- Passive isolation, the padded cushions themselves. The ear cups and their foam physically block and absorb sound, turning it into a whisper of heat in the material. That’s a barrier, not a cancellation, and it’s the part that actually handles the high frequencies the electronics give up on [3]. Real headphones use both, which is exactly why the two get confused.
- Earplugs. Same family as the cushions: foam or silicone that blocks and absorbs the pressure wave before it reaches your eardrum. No microphone, no anti-noise, nothing added. If it works with dead batteries, it isn’t active cancellation.
- Playing music or white noise to drown it out. This is masking, and it’s the “play a louder noise over it” idea done deliberately. It adds sound energy so your brain stops attending to the noise underneath, but the noise is still fully there, and the room is genuinely louder. It’s the opposite of cancellation: masking piles waves on, cancellation takes them away.
The tell for a false friend is simple. Ask whether an equal-and-opposite wave is being added to bring the total down. Cushions, plugs, and masking all say no.
Fun consequences
| Observation | Why |
|---|---|
| The engine drone dies but the crying baby cuts through | Low steady frequencies cancel well; high, sharp, unpredictable sounds outrun the fixed delay. |
| Cancellation needs power; earplugs don’t | Sampling, inverting, and playing anti-noise is active work. A dead battery leaves you with only the passive seal. |
| A poor fit ruins even good headphones | The high end is handled by the physical seal, and the inside feedback mic can only correct the sound that reaches its sealed pocket, so a leak lets the sounds the electronics can’t catch pour straight in. |
| Some people feel a faint “pressure” with ANC on | The steady anti-noise field changes what your eardrum feels; there’s no actual pressure change, but the ear can read it as one. |
| It’s better on a plane than in a café | A jet cabin is a wall of steady low-frequency drone, the ideal target; a café is bursts of clattering high-frequency chatter, the worst case. |
| Turning it on can make a high whistle slightly worse | Past a certain frequency the mirror arrives out of step and adds instead of cancels, exactly as the demo shows. |
So the next time the cabin roar drops away when you press the button, you can enjoy the genuinely odd truth of it: the headphones got quieter by making more sound. They listened to the wave, drew its mirror image, and handed it back to your ear so the two could add up to nothing. Blocking is what the padding does. Cancelling is arithmetic, performed on a wave, a few hundred times a second.
Lunch Break Physics runs Tuesdays at noon. Last week: why the shower curtain attacks you. Next Tuesday: why a curveball curves. Got an everyday-physics puzzle you’d like poked at? The comments are open.
Sources
- [1] Understanding Sound — U.S. National Park Service — sound travels through air as a wave described by frequency (pitch, in hertz) and amplitude (loudness, in decibels); humans hear roughly 20 Hz to 20,000 Hz, and decibels are logarithmic, so a 10 dB rise is a ten-fold jump in sound level.
- [2] Superposition and Interference — OpenStax College Physics 2e (§16.10) — when waves overlap their disturbances add (superposition); two identical waves in phase produce constructive interference at twice the amplitude, and two identical waves exactly out of phase produce pure destructive interference in which the resulting amplitude is zero and the waves completely cancel.
- [3] Active Noise Reduction — FizziQ glossary, How Active Noise Cancellation Works, and What It Cannot Cancel — Sound Control Technologies, and Active Noise Control (reference and error microphones) — MathWorks documentation — active reduction superimposes an equal, phase-opposed wave (destructive interference), effective mainly on low frequencies and complementing the passive attenuation of the ear cushions; systems use a feedforward reference microphone and/or a feedback error microphone driving an adaptive filter that minimises the residual, and a fixed processing delay stays close enough in phase to cancel a low tone but throws a short-wavelength ~4 kHz tone out of phase so it adds instead of cancelling.
About the Author
Stefan Christoph is a Principal Solutions Architect at AWS, focused on agentic AI, media & entertainment, and helping builders move from demo to production. He writes about AI architecture, developer productivity, and the future of software.
This is a personal blog. Opinions expressed here are my own and do not represent the views or positions of my employer.
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