How Does Noise Cancelling Work? Silence by Adding Sound

A sound wave is a sequence of compressions and rarefactions travelling through the air, and its pressure at any point rises and falls in a pattern. Add a second wave of the same pattern shifted by half a cycle, so that its compressions coincide with the first wave's rarefactions, and the pressures add to zero: this is destructive interference, the same phenomenon that makes dead spots in a concert hall and the dark bands in a physics demonstration with two slits. Active noise control generates that second wave deliberately, which requires measuring the first one, computing its inverse, and playing the inverse so that it arrives at the ear at exactly the same moment as the original, with the same amplitude and the opposite sign.

The parts:

• •A microphone on the outside of each earcup, which picks up the ambient sound a fraction of a millisecond before it reaches the ear through the cup
• •A processor that inverts the signal and adjusts its size and timing for the path through the cup, which is fixed for a given headphone and tuned by the manufacturer
• •The speaker, which plays the inverted signal mixed with the music
• •In better designs, a second microphone inside the cup that hears what actually reached the ear, so that the processor can correct its output continuously, feedback rather than feedforward
• •The earcup itself, whose seal and padding block the high frequencies that the electronics cannot

The cancellation must be precise to a fraction of a wavelength, and the wavelength of a sound shrinks as its pitch rises. A 100-hertz drone has a wavelength of about three and a half metres, so an error of a centimetre in the anti-noise's timing is negligible and the drone is cancelled by twenty or thirty decibels; a 2,000-hertz voice has a wavelength of seventeen centimetres, and the same centimetre is a large fraction of it, so the anti-noise arrives out of step and may even add to the sound. High frequencies also enter the cup by paths the microphone did not measure and vary from moment to moment, and the processor cannot predict a sound it has not yet heard. The result is that the technology is superb against the steady, low roar of engines, trains, air conditioning and road noise and weak against speech, crying babies and clatter, which is why the cabin goes quiet and the person in the next seat is still audible, and why the passive seal of the cup does the work above about a kilohertz.

Paul Lueg, a German physician, patented the idea of cancelling sound with inverted sound in 1936, with drawings of a loudspeaker silencing a duct, and it could not be built with the electronics of the time. Analogue systems were tried on helicopter pilots' headsets in the 1950s, and the modern product began in 1978, when Amar Bose, flying to Europe with a pair of the airline's headphones, could not hear the music over the engines and sketched the circuit on the plane; his company sold the first commercial noise-cancelling headset to pilots in 1989 and to passengers in 2000. Digital processing made the earbud versions of the 2010s possible, with adaptive filters that adjust to the wearer's ear and the sound around them, and the same principle, with larger speakers, quiets aircraft cabins, car interiors, ventilation ducts and the MRI scanner, where it protects the patient from the machine's hammering.

Wearers often report a sensation of pressure when the cancellation switches on, which is not pressure but the brain's reaction to the sudden loss of low-frequency sound it had been filtering; the processor also adds a faint hiss and, in feedforward designs, can amplify wind noise on the microphones, which is why walking in a breeze with the cancellation on can be louder than off. The technology does not create silence, only the reduction of the parts of the noise it can predict, and the quiet it produces on a long flight is the absence of a roar that the wearer had stopped noticing until it was gone. The physics is a century old; the earbud that carries it is a small computer whose whole job is to be exactly wrong.

Noise cancelling works by destructive interference: a microphone on the earcup hears the surrounding noise, a processor inverts it and a speaker plays the inverse, so that the original and its mirror image cancel at the eardrum. Because the timing must be exact to a fraction of a wavelength, it cancels low, steady sounds such as engines and air conditioning by tens of decibels and does little against voices and sudden clatter, which the passive seal of the cup handles; the idea was patented in 1936 and made practical by Bose in 1989.