Superposition, interference, standing waves, and the Doppler effect

When two waves overlap, their displacements add together, the principle of superposition. If crest meets crest, they combine into a bigger wave (constructive interference); if crest meets trough, they partly or completely cancel (destructive interference), the idea behind noise-canceling headphones. A standing wave forms when waves reflecting back and forth in a confined space, like a guitar string fixed at both ends, interfere so that some points (nodes) stay still and others (antinodes) vibrate strongly; a string can only form standing waves at certain frequencies, which is why it plays specific notes. The Doppler effect is the change in observed frequency when a wave source and observer move relative to each other: a siren sounds higher-pitched as it approaches and lower-pitched as it moves away, and light from galaxies moving away from us is shifted toward the red end of the spectrum.

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