# Dictionary:Wave equation

{{#category_index:W|wave equation}}
An equation that relates the spatial and time dependence of a disturbance which can propagate as a wave. In rectangular coordinates *x*, *y*, *z*, it is

where represents wave displacement (pressure, rotation, dilatation, etc.) and *V* the velocity of the wave. Functions are solutions to this equation.

In spherical coordinates where *r* is the radius, the colatitude, and the longitude, the wave equation becomes:

The foregoing are forms of the **scalar wave equation** These forms do not provide for the conversion of P-waves to S-waves nor vice-versa.

The **vector wave equation** is more general; for isotropic media it is

which can be written in component form as

If , this gives an S-wave; if , a P-wave. The wave equation in polar anisotropic (transversely isotropic) media is given in Figure T-13.

For a derivation, and the relation of the *wave equation* to the *equation of motion*, see the main page: Wave equation.