Superposition principle

A property of every linear system: if y₁(x,t) and y₂(x,t) both satisfy the governing equation, so does y₁ + y₂. For waves, this means two disturbances on the same medium simply add together wherever they overlap, then continue unchanged along their separate paths.

Superposition is the reason music is intelligible, radio signals can share the spectrum, and two laser beams cross without scattering. It is a direct consequence of the linearity of the wave equation, Maxwell's equations in vacuum, and Schrödinger's equation. When the underlying equations are non-linear — shock waves in gas, rogue waves at sea, solitons in optical fibres — the principle fails, and overlapping waves scatter, steepen, or merge instead of passing cleanly through each other.