Superposition and Interference

When two or more waves meet at the same point, the resulting displacement is found by adding the individual displacements. This deceptively simple rule — the principle of superposition — gives rise to the rich phenomena of interference and is the key to understanding Young's double-slit experiment.

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The Principle of Superposition

The principle of superposition states that when two or more waves overlap, the resultant displacement at any point is the vector sum of the individual displacements due to each wave at that point.

If two crests arrive at the same point simultaneously, their displacements add to produce a larger crest. If a crest and a trough of equal amplitude arrive together, they cancel each other out, and the resultant displacement is zero.

This principle applies to all types of wave — sound, light, water, and electromagnetic — and it works regardless of how many waves are overlapping.

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Constructive and Destructive Interference

Constructive interference occurs when two waves arrive in phase (crest meets crest, or trough meets trough). Their amplitudes add together, producing a resultant wave with a larger amplitude. If both waves have amplitude A, the resultant has amplitude 2A.