Wave Equation

see also:

• Fundamental Partial Differential Equations

The wave equation describes the propagation of waves (e.g., sound waves, electromagnetic waves) through a medium. It is a second-order hyperbolic PDE:

$\frac{{\partial }^{2}u}{\partial t^2}=c^2{\nabla }^{2}u$

where $u$ is the wave function, $c$ is the speed of the wave in the medium, and ${\nabla }^2$ is the Laplacian.