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Superposition Principle

Any function ƒ which satisfies the wave equation represents a wave; ƒ is called a wave function. In general, if there are several wave functions ƒ₁, ƒ₂, …., ƒ_n, then a linear sum of these functions also satisfy the wave equation. That is, if

where, F = ƒ₁ + ƒ₂ + …. + ƒ_n. This is called the principle of superposition of waves.

The above principle means that if there are several waves ƒ₁ …. ƒ_n simultaneously propagating through a medium, than their resultant also represents a wave motion. Further, the net displacement F of any point in the medium at any time, is the algebraic sum of displacements due to all the different waves: F = ƒ₁ + …. + ƒ_n.