How Does Noise Cancelling Erase Sound?
– The Idea of Adding Sound to Remove Sound
Put on noise-cancelling earphones on a train or plane, and the low roar of the engine suddenly goes quiet. Ordinary earplugs simply block your ears. Here, you can still hear things, yet that low drone alone vanishes cleanly. The reason is that the earphones are not blocking the sound. They are adding another sound to cancel it.
The moment you switch noise cancelling on, the low rumble around you may seem to shrink, as if someone turned down a volume knob.
The odd thing is that nothing about your ears' surroundings has changed. The earphones seal your ears no more than before, yet certain sounds (a low engine hum, a ventilation fan) fade away as if they were singled out.
If the sound isn't being blocked, what is going on?
Sound is a wave in which air pressure rises and falls, over and over.
Add a wave whose peaks and troughs are exactly reversed, and the two waves cancel each other and almost disappear.
Noise cancelling is technology that creates this "wave cancellation" artificially, using an electronic circuit.
Sound is a wave of vibrating air pressure
Sound is vibration in which air pressure rises and falls, again and again. When you hit a drum, the air vibrates, the vibration travels to your ear as a wave, and it shakes your eardrum. That is how we hear it.
A wave has peaks (where pressure is high) and troughs (where pressure is low). Like the Doppler effect, which changes the pitch you hear, sound travels through the air as an invisible wave.
Add an exactly opposite wave, and the wave vanishes
This is the heart of noise cancelling. Add a wave and another with peaks and troughs swapped (an opposite-phase wave) at the same place at the same time. Peaks are cancelled by troughs, and troughs by peaks, leaving a nearly flat line. This is called "destructive interference," or "cancellation by opposite phase."
Noise-cancelling earphones have small microphones facing outward. A microphone picks up the noise around you, and an internal electronic circuit works out, in a very short time, an "opposite-phase sound" whose peaks and troughs are exactly reversed from that noise. The speaker then plays that sound, and it is thought to cancel the original noise just in front of your eardrum.
In other words, the sound is not physically blocked. It is cancelled by "meeting it with the opposite sound." That is why only certain sounds go quiet even though the seal on your ears hasn't changed.
It adds the exact opposite sound to the original, so you can't hear it.
Why are low sounds easy to cancel and high sounds hard?
Noise cancelling works well on low, steady sounds such as engines and ventilation fans. It is known to work poorly on human voices and the high clink of dishes.
The reason is that a tiny amount of time (a processing delay) passes between the microphone picking up the sound and the earphone playing the opposite-phase sound. If this delay is not negligible compared with the time one vibration takes (the period), the timing of the opposite phase slips, and the cancelling fails.
A low sound takes a long time for one vibration, so even with a small processing delay, the timing slip is hardly noticeable and cancelling is easy. A high sound finishes one vibration quickly, so the same delay becomes a relatively large timing slip, and cancelling is harder. The fold-out below uses numbers to check how high a pitch the effect reaches.
Noise cancelling is technology that weakens certain steady sounds. It does not erase every sound around you. Sudden sounds (a car horn, someone calling out) are hard to cancel and are thought to come through as they are. When you need to stay aware of your surroundings, such as while walking or cycling, use it with these features in mind.
What you can check yourself
- Set up your phone so you can play the same music or sound on two devices at once (if you have none, one device and a speaker can still give you hints)
- If you have noise-cancelling earphones or headphones, switch them on and off in a quiet room and compare how the sound of a fan or air conditioner changes
- Compare a low, steady sound (a fan, an air conditioner) with a high, short sound (a finger snap, dishes) and see whether the effect differs
If the low, steady sound seems to go clearly quieter, you have felt for yourself the point made above: that low sounds are easier to cancel.
Summary
Noise cancelling is technology that does not physically block sound. It builds a wave exactly opposite to the noise the microphone picked up (an opposite-phase sound) and adds it just before the eardrum to cancel it. Processing takes time, however small, so low sounds with long vibrations are easier to cancel, and high sounds with short vibrations are harder.
Noise cancelling is not magic that creates silence.
It reads the wave and hits it with its exact mirror image, a race of precise timing.
For those who want to know more – terms, numbers, and links to textbooksFrom middle-school science to current research, each level is clearly labelled
- Middle schoolCovered in middle-school science
- High schoolCovered in high-school "Basic Physics"
- High school+High-school "Physics," or material treated as an advanced topic or sidebar in textbooks
- UniversityUniversity-level specialist subjects (signal processing, acoustic engineering) not taught in high school
- ResearchTopics researchers are studying right now, not yet taught as settled knowledge even at university
Middle schoolTerms: words about waves and sound
- Wave: a phenomenon in which the state of a place (here, air pressure) changes periodically and the change travels onward.
- Amplitude: the height of a wave's peak (the size of the vibration). For sound, it corresponds to loudness.
- Period: the time one vibration of a wave takes.
- Frequency: the number of vibrations per second. It is the inverse of the period, and its unit is Hz (hertz).
High schoolChecking with a formula: how high a pitch can be cancelled?
By comparing the processing delay, from the microphone picking up sound to the opposite-phase sound being played, with the period of the sound, we can estimate roughly how high a pitch can be cancelled well.
Period = 1 ÷ Frequency
| Period | The time one wave vibration takes. Unit: seconds |
| Frequency | The number of vibrations per second. Unit: Hz |
| Processing delay | The time from the microphone picking up sound to the opposite-phase sound being played. Unit: seconds |
To keep the timing slip small, the "processing delay" must be short enough compared with the "period." As a rule of thumb, we set the condition that "the processing delay is at most one tenth of the period" and calculate from there.
The processing delay of noise cancelling varies with the model and method, but a typical rough figure is about 100 microseconds (0.0001 seconds). We use this value in the calculation.
| Processing delay (rough) | 0.0001 seconds |
| Period needed (at least 10 times the delay) | 0.0001 × 10 ＝ 0.001 |
| Period needed | 0.001 seconds or more |
| Frequency for this period | 1 ÷ 0.001 ＝ 1000 |
| Upper limit of easily cancelled sound (rough) | About 1000 Hz (1 kHz) |
This calculation gives a rule of thumb: sounds lower than about 1000 Hz are easy to cancel, and sounds higher than that are harder. The low drone of planes and engines mostly lies below this range, which is why noise cancelling is said to work well on it. By contrast, human voices (rich in higher-frequency parts, especially consonants) have many parts above this range and are hard to cancel, it is sometimes explained.
* The actual processing delay varies with model and method, and the value here is a typical rough figure. The "one tenth of the period" criterion is also a simplified rule of thumb for understanding the mechanism, and differs from real design standards.
High school+Thinking of it as a phase shift
The main text and steps ① and ② described this as a "time shift," but in the study of waves it is usual to treat it as a "phase shift." An opposite-phase sound is shifted by half a period (180 degrees in phase) from the original. With a processing delay, this 180-degree shift is no longer exactly 180 degrees, and the cancelling is incomplete. If the error grows too large, the sound can even be reinforced instead of cancelled, it is said.
UniversityFeedforward and feedback methods
Real noise cancelling uses a "feedforward method," in which a microphone outside the ear picks up surrounding sound ahead of time and processes it, and a "feedback method," in which a microphone inside the ear (nearer the eardrum) measures the sound actually reaching the eardrum and keeps correcting it. Many products are said to combine the two.
Signal processing called adaptive filtering is also used, which fine-tunes the cancelling to the character of the surrounding sound. It is a way of coping with real environmental sound that changes over time, rather than a simple sound whose nature is fixed in advance.
ResearchWhat is still unclear, and what is still being developed
- How far irregular, fast-changing sounds (non-stationary sounds), such as voices and dishes, can be cancelled is still under research and development. Cancelling these effectively is technically harder than cancelling low, regular sounds.
- How to suppress "wind noise," a problem when walking outdoors, is also a challenge still under development. Noise made by wind hitting the microphone directly differs in nature from ordinary noise and is hard to handle.
- Research also continues on "sound zones," technology that quiets one spot without earphones. It uses multiple speakers to cancel sound in one place while leaving it normal in another, but many technical problems are said to remain before practical use.
The basic idea of "adding sound to remove sound" is old, but making it work on any sound, in any place, is technology still under research.
Links to textbooks (by level)
| Level | Subject / unit | Where in this article |
|---|---|---|
| Middle school | Science: properties of sound | Basic terms: wave, amplitude, period |
| High school | Basic Physics: properties of waves | Calculation estimating the upper limit of cancellable sound from period and frequency |
| High school+ | Physics: wave interference | Explanation as a phase shift |
| University | Acoustic engineering, signal processing | Feedforward / feedback methods, adaptive filters |
| Research | Acoustic engineering (in development) | Handling non-stationary sounds, wind-noise countermeasures, sound-zone technology |
- Explanations of the basic principle of active noise control in acoustic engineering textbooks.
- Kuo, S. M. & Morgan, D. R., Active Noise Control Systems: Algorithms and DSP Implementations (a standard technical account of noise cancelling using adaptive filters).
- General-audience explanatory materials on the principle of noise cancelling from major headphone and earphone makers.
- Explanations of the superposition principle and interference of waves in physics textbooks.
- Research explanations of "personal sound zone" technology in acoustic engineering.
* The processing delay and cancellable frequency are typical figures for understanding the mechanism. Actual performance varies with model and method.
* This article is a general-audience science explainer. Noise cancelling does not block all surrounding sound. When you need to stay aware of your surroundings, such as while walking or cycling, follow each product's manual and guidance.