How do noise-cancelling headphones erase sound by adding more sound?

Noise-cancelling headphones fight sound with sound. A tiny microphone listens to the noise around you, and the headphones play a second sound designed to cancel it out. The two meet at your ear and, if the timing is right, they largely erase each other.

Here is why that works. Sound is a pressure wave: a rapid series of squeezes and stretches of the air. The headphones produce a wave with the same size but flipped upside down, so every squeeze from the noise meets a stretch from the headphones. The waves add together and cancel, an effect physicists call destructive interference. It's like one person pushing a swing while another pulls it back with the same force: the swing barely moves.

This works brilliantly on steady, low rumbles like aircraft engines, air conditioning and road noise, because a repeating sound is easy to predict. Sudden or irregular sounds such as voices and alarms are much harder. High-pitched sounds have short wavelengths, and cancelling them would require electronics closer to your eardrum than is currently feasible. So good headphones also rely on old-fashioned padding and seals to block the high notes.

The idea is almost a century old: Paul Lueg received the first patent for a noise control system in 1936. The consumer version owes a lot to a disappointing flight. In 1978 Amar Bose was handed a pair of headphones on a flight that failed to drown out the plane's noise, and he came up with a design for active noise cancelling. His company's QuietComfort headphones reached ordinary shoppers in 2000.