The wave equation is the important partial differential equation
 | (1) |
that describes propagation of waves with speed 
. The form above gives the wave equation in three-dimensional space where 
is the Laplacian, which can also be written
 | (2) |
An even more compact form is given by
 | (3) |
where 
is the d'Alembertian, which subsumes the second time derivative and second space derivatives into a single operator.
The one-dimensional wave equation is given by
 | (4) |
As with all partial differential equations, suitable initial and/or boundary conditions must be given to obtain solutions to the equation for particular geometries and starting conditions.
