Active noise reduction cancels a noise by superimposing on it a wave of the same amplitude in phase opposition: this is destructive interference. Effective mainly on low frequencies, it complements the passive attenuation of the ear cushions, which handles the high frequencies.
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How to measure it in class
FizziQ combines a sound level meter and a frequency synthesizer: you can emit two identical sounds, vary the phase shift between them and measure the resulting level. This is the most direct way to observe that one sound plus one sound can produce silence.
Steps:
- Connect two identical loudspeakers to two devices, or use the two channels of a stereo speaker
- Use FizziQ’s synthesizer to emit the same low-frequency pure tone on both channels, for example 200 Hz
- Place the smartphone sound level meter at equal distance from the two sources and record the level in dB
- Reverse the polarity of one of the two channels (swap the two loudspeaker wires): the waves switch to phase opposition
- Record the level again: it should drop sharply at the equilibrium point
- Move the sound level meter a few centimeters and observe that the cancellation disappears, then repeat at 2,000 Hz to compare
Scientific activities on this topic
- Destructive sound interference: create a noise-free bubble - build your own noise attenuator and discover how noise-canceling headphones work
- Acoustic beats 440/441 Hz
- Adding sound levels (dB)
Learn more
How do the headphones produce the anti-noise?
The chain has three elements. A microphone picks up the outside noise. A processor inverts the signal, that is, multiplies it by −1, and corrects it to compensate for the path and the delays of the system. A loudspeaker, the very one that plays the music, emits this inverted signal. At the eardrum, the noise wave and the anti-noise wave superimpose and their sum is close to zero.
Everything depends on the precision of the timing. For the cancellation to work, the anti-noise must reach the eardrum exactly in phase opposition with the noise. A phase error is paid for immediately: at a phase shift of 60° the attenuation is only a few decibels, and beyond 120° the superposition reinforces the noise instead of canceling it.
Why only low frequencies?
This is the fundamental limit, and it is purely geometric. The microphone is not in the same place as the eardrum: there is typically 1 to 3 cm between the two. The system must therefore predict what the noise will be at the ear from what it picks up a few millimeters away, and do so within a few tens of microseconds.
As long as the wavelength is large compared to this distance, the noise is almost identical at both locations: the correction remains valid. This is the case below approximately 1 kHz, where λ exceeds 34 cm - ten times the microphone-ear gap. On the other hand, at 5 kHz, λ is only 6.9 cm: between the microphone and the eardrum, the wave has already traveled a significant fraction of its period, and the calculated phase is no longer correct. The system can no longer guarantee phase opposition, and the cancellation ceases to be reliable. Added to this is the latency of the digital processing, which also becomes comparable to the period of the signal.
In practice, good headphones achieve 20 to 30 dB of active attenuation between 50 and 500 Hz, only a few decibels beyond 1 kHz, and nothing at all at 5 kHz.
What about the high frequencies, then?
They are handled differently: by passive attenuation. The cushions, the foam and the rigid shell of the headphones reflect and absorb short waves, which penetrate dense materials poorly. Passive isolation is good above 1 kHz and mediocre below - exactly the opposite of active isolation. The two techniques are therefore complementary, and it is their combination that gives travel headphones their comfort. Open noise-canceling headphones, without enveloping cushions, would be disappointing on voices.
A history older than one might think
The principle was patented as early as 1933-1936 by the German engineer Paul Lueg, well before electronics capable of implementing it existed. The first practical realizations date from the 1950s, in the aeronautical context: Lawrence Fogel worked on headsets for helicopter crews, where rotor noise is intense and very low-pitched - therefore ideal for anti-noise. The general public only gained access to it from the 1980s-1990s.
Anti-noise and beats: do not confuse them
Two sounds in phase opposition cancel each other because they have the same frequency. Two sounds of slightly different frequencies, on the other hand, produce beats: the amplitude periodically passes through minima, but the sound is never durably extinguished. Noise-canceling headphones rely on the first phenomenon, not the second.
Does adding two sounds really increase the sound level by 3 decibels? (FizziQ blog) deals with the case of coherent sources, the one that makes anti-noise possible.
Formula
Ideal anti-noise signal, opposite of the captured noise:
s_anti(t) = − s_noise(t)
For a pure tone, this is equivalent to a phase shift of half a period:
s_anti(t) = A × sin(2πft + π)
Superposition of two waves of the same frequency, with amplitudes A₁ and A₂, phase-shifted by φ - the resulting amplitude is:
A = √(A₁² + A₂² + 2A₁A₂ × cos φ)
Special cases: φ = 0 gives A = A₁ + A₂ (constructive interference); φ = π with A₁ = A₂ gives A = 0 (total destructive interference).
Wavelength, which sets the size of the cancellation zone:
λ = v / f
where:
- s(t): acoustic pressure signal at time t (Pa)
- A: amplitude of the wave (Pa)
- f: frequency (Hz)
- φ: phase shift between the two waves (rad)
- λ: wavelength (m)
- v: speed of sound, approximately 343 m·s⁻¹ in air at 20 °C
Application examples
- Travel headphones: aircraft cabin noise is dominated by components from 60 to 300 Hz. At 100 Hz, λ = 3.4 m, very large compared to the microphone-eardrum gap: anti-noise is very effective there, with 25 to 30 dB gained. The captain’s announcements, however, remain audible - their spectrum is too high-pitched.
- Voices of neighboring passengers: located between 300 Hz and 3 kHz, they are only weakly attenuated by the active part. What reduces them is the cushion.
- Car interiors: some cars play through the onboard loudspeakers an anti-noise tuned to the engine speed, measured by the engine control unit. The frequency to be canceled is known in advance, which makes the task simpler than with random noise.
- Order of magnitude of the limit frequency: with 2 cm between microphone and eardrum, the condition “λ ≫ d” ceases to be satisfied around 1 to 2 kHz. This is precisely the range where the drop in effectiveness of commercial headphones is observed.
- Passive worksite ear defenders: they achieve 25 to 30 dB of attenuation above 1 kHz by simple isolation, without any electronics - proof that passive is enough in the high frequencies.
- Room-scale limit: canceling noise in an entire room is out of reach, because phase opposition would have to be maintained at every point simultaneously. Anti-noise only works in a small volume around the ear.
FAQ
Q: Why don’t noise-canceling headphones suppress voices? A: Because voices occupy a frequency range that is too high, between approximately 300 Hz and 3 kHz. Above 1 kHz, the wavelength becomes comparable to the distance between the headphone microphone and the eardrum, and the system can no longer correctly calculate the phase of the wave to be canceled. Only the passive isolation of the cushion acts then.
Q: Can two sounds really produce silence? A: Yes, provided they have the same frequency, the same amplitude and a phase shift of half a period. The energy is not destroyed for all that: it is redistributed in space or sent back toward the sources. And the cancellation is only total at one point, never everywhere.
Q: Can the headphones increase the noise instead of reducing it? A: Yes, if the phase is miscalculated. A phase shift greater than 120° turns destructive interference into constructive interference. This is why some cheap headphones produce a slight hiss or an unpleasant sensation of pressure at certain frequencies.
Q: Do you need very isolating headphones if the reduction is active? A: Yes, both are indispensable and complementary. The active part handles the low frequencies, where passive isolation is ineffective; the passive part handles the high frequencies, where the active part no longer works. Active noise-canceling headphones without good mechanical isolation would be disappointing.
Q: Why aren’t anti-noise systems installed in homes near airports? A: Because the cancellation is only valid in a small volume around the point where the phase is controlled, on the order of the wavelength. Covering an entire room would require a network of microphones and loudspeakers impossible to calibrate in real time. Passive isolation is preferred: double glazing, noise barriers.
Related concepts
Interference - Phase Shift - Wavelength - Sound Intensity - Decibel - Microphone - Acoustic Beat