### Solving the 2D Wave Equation

Since solving the wave equation in 2D has all the essential features of the 3D case, we will look at the 2D case in this section.

Specializing Eq.(B.47) to 2D, the *2D wave equation* may
be written as

The 2D wave equation is obeyed by *traveling sinusoidal plane
waves* having any amplitude , radian frequency , phase
, and direction
:

*dispersion relation*:

^{B.36}

The sum of two such waves traveling in opposite directions with the
same amplitude and frequency produces a *standing wave*. For example,
if the waves are traveling parallel to the axis, we have

which is a standing wave along .

**Next Section:**

2D Boundary Conditions

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Vector Wavenumber