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Principle of superposition
Beginner
Displacements of overlapping waves add.
y = y₁+y₂When waves overlap, the resulting displacement is the sum of the individual ones. They pass through each other unchanged.
Two pulses on a string cross and continue.
Applies to linear media only.
In more detail
The principle of superposition states that when waves overlap, the resultant displacement is the sum of the individual displacements. This holds for linear waves.
Real-world uses
- Noise-cancelling headphones add a wave out of phase with the noise.
- Music is the superposition of many sound waves at different frequencies.
- Noise-cancelling headphones use superposition to add an anti-phase copy of the noise, which reduces what reaches your ear.
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Frequently asked questions
Does superposition always apply?
For linear systems, yes. Very large amplitudes can break linearity.
Do waves pass through each other?
Yes, they superpose during overlap and then continue unchanged.
Do overlapping waves always add to something larger?
No. Overlapping waves add their displacements at each point, so they can increase, reduce or cancel each other.
Related topics in Waves & Sound
Phase change on reflection · Refraction of waves · Diffraction · Constructive and destructive interference · Path difference and phase · Beats