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.
