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Three-Dimensional Wave Equation

We have already seen that the one-dimensional plane wave solution, (529), satisfies the one-dimensional wave equation,

$\displaystyle \frac{\partial^2\psi}{\partial t^2} = v^2\,\frac{\partial^2\psi}{\partial x^2},$ (536)

where $ v$ is the characteristic wave speed of the medium through which the wave propagates. (See Section 7.2.) Likewise, the three-dimensional plane wave solution, (533), satisfies the three-dimensional wave equation (see Exercise 1),

$\displaystyle \frac{\partial^2\psi}{\partial t^2} = v^2\left(\frac{\partial^2}{...
...^2}+\frac{\partial^2}{\partial y^2}+\frac{\partial^2}{\partial z^2}\right)\psi.$ (537)

Richard Fitzpatrick 2013-04-08