What happens when two waves arrive at the same point in space at the same time? The answer is surprisingly simple: the waves do not “collide” with or disturb one another, but their perturbations add up point by point. At a given instant and a given point, the displacement of the medium is the algebraic sum of the displacements each wave would produce on its own.
Principle — Superposition
The resulting perturbation is the sum of the individual perturbations:
The remarkable point is that, after overlapping, the waves each carry on along their own way as if nothing had happened: they pass through each other without being altered. The sum holds only at the instant and place where they coexist. It is precisely this combination — adding up where they meet, ignoring each other elsewhere — that generates stable interference patterns and repeated figures.
From this single principle follow two fundamental phenomena that we will study next: interference, which arises from the superposition of waves with the same frequency, and beats, which arise when the frequencies are slightly different.
Note
The superposition principle holds as long as the medium responds linearly, that is, as long as the amplitudes are not too large. For very intense waves (for example a shock wave) simple superposition is no longer exact.
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Topics: Onde Skills: Principio di sovrapposizione
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