How headphones erase noise by producing more sound.
A microphone on the headphone measures outside noise. A chip calculates what part would reach your ear and plays exactly the same wave flipped: peak against trough. The two cancel out, called destructive interference. It works best on low, steady hums like jet engines. Paul Lueg patented the idea in 1936; headphones have existed since the late 1980s.
Useful: ANC does little against voices or crying babies: high tones have wavelengths too short to cancel cleanly.
Source: en.wikipedia.org