Have you ever put on noise-cancelling headphones on a train or aeroplane and noticed that the background rumble suddenly becomes much quieter? The headphones have not stopped the engines, wheels or air-conditioning system from making sound. Instead, they use the physics of waves to reduce some of the sound reaching your ears. Sound travels through air as changing pressure. When two sound waves reach the same place at the same time, their effects combine. This is called the principle of superposition. The resulting disturbance depends on the displacement or pressure change produced by each wave at that moment. If two waves reinforce each other, they produce constructive interference and the resulting amplitude can become larger. But if one wave produces a pressure increase while another produces a matching pressure decrease, they can partially or almost completely cancel. This is called destructive interference. Active noise-cancelling headphones use this idea. Tiny microphones detect some of the sound around you. Electronics analyse the signal, and the headphone speakers produce another sound designed so that its pressure variations oppose the unwanted sound when the waves reach your ear. When the original noise and the generated sound overlap, superposition reduces the amplitude of the resulting pressure variations. Less variation in air pressure at your eardrum means the unwanted sound can seem much quieter. Perfect cancellation is difficult. Real sounds contain many frequencies and can change very quickly. Active noise cancellation is particularly effective against relatively steady, lower-frequency sounds such as engine noise, air-conditioning systems and the rumble inside trains and aircraft. The physical material of the headphones can also block some sound through passive noise reduction. Superposition is not only used to make things quieter. When waves reinforce one another, constructive interference can make the resulting disturbance larger. The same principle helps produce standing waves in musical instruments and interference patterns with light and water waves. Noise-cancelling headphones therefore do something rather clever: instead of only trying to block unwanted sound, they produce carefully controlled sound of their own. Two sounds can combine to produce less sound at a particular place—all because waves obey the principle of superposition.