Two identical sines can cancel to silence or double in volume depending on their phase, the same interference that powers noise-cancelling headphones.
In the world
Noise-cancelling headphones work by playing an inverted copy of ambient sound: two waves, opposite phase, near-silence.
Phase is where in its cycle a sine starts. One sine plus a copy of itself doubles the amplitude; one sine plus its inverted copy cancels to silence. Your ear cannot hear the phase of a lone sine, but it can hear the result of two interacting.
This is the hidden partner of amplitude. Every additive recipe is technically a list of amplitudes and phases, though for most musical work the phases matter far less than the amplitudes.
Did you know?
Bose's first noise-cancelling headphones were invented in 1986 after founder Amar Bose endured a noisy transatlantic flight. The technology is literally phase cancellation - the same physics you see on the right.
Explore
Three scrolling waveforms: Wave 1 (cyan) is fixed, Wave 2 (magenta) you control. Drag left/right to shift Wave 2's phase. The gold SUM line at the bottom shows the result. At 0 degrees it doubles. At 180 degrees it cancels to flat silence. Click to snap between key angles.