Noise-cancelling headphones use destructive interference to cancel out external sounds. When sound waves travel, they create areas of high and low pressure as they oscillate. The headphones work by creating a sound wave that is the exact opposite of the external sound wave, causing the two waves to cancel each other out. This is known as destructive interference. By using this technique, noise-cancelling headphones are able to reduce or eliminate the amount of external sound that reaches the ear of the listener.