Wave equation

Summary

The wave equation $u_{tt} = c^2 \Delta u$ is the basic hyperbolic partial differential equation. It describes vibrating strings and membranes, sound, and light in vacuum. Its solutions travel at the finite speed $c$. In one space dimension every solution is a sum of a wave moving left and a wave moving right. It is the model for the theory of hyperbolic equations, just as the heat equation is for parabolic ones.