Wave Equation

Form

For a scalar field $\psi(x,t)$,

$$\frac{\partial^2 \psi}{\partial t^2} = v^2\nabla^2\psi.$$

Electromagnetic Waves

In vacuum, Maxwell’s equations imply

$$\nabla^2\mathbf E-\mu_0\varepsilon_0\frac{\partial^2\mathbf E}{\partial t^2}=0.$$

Thus light propagates at $c=1/\sqrt{\mu_0\varepsilon_0}$.