How can headphones reduce sound with more sound?

Adding another sound can sometimes make a noise smaller. Active noise-canceling headphones use microphones to sense sound and electronics to control a small speaker. Their goal is to produce an opposing pressure variation near the listener’s ear.

Sound makes pressure rise and fall around its ordinary background value. When two sounds overlap, their pressure variations add. If one variation rises while the other falls by the same amount at the same place, their sum can be much smaller. This is destructive interference.

In the illustration, one repeating noise has an amplitude, or largest pressure variation from background, of 1 pascal. A pascal is a unit of pressure. An ideal opposing wave of the same amplitude, timed half a cycle apart, gives a zero sum at the stated observation point. Half that opposing amplitude leaves a 0.5-pascal amplitude. Matching the timing matters as much as matching the size.

Real sound contains many frequencies, and microphones, processing and speakers have delays and limits. Headphone seals also reduce sound by a separate, passive mechanism. Cancellation is not silence everywhere or destruction of all sound energy: it changes the combined sound field locally, and steady background sounds are generally easier to reduce than rapidly changing ones.