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This is an old revision of this page, as edited by Hillman (talk | contribs) at 03:14, 27 May 2005 (D'Alembert's general solution to the 1D wave equation is not the wave equation itself!). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

A pedantic quibble: the author of this article says that

${\displaystyle U(x,t)=f(kx+ct)+g(kx-ct)}$

is the wave equation. But of course this is the D'Alembert general solution to the one-dimensional wave equation, not the equation itself, is often written in coordinate-free notation as

${\displaystyle \Box U=0}$

(where ${\displaystyle \Box }$ is the Laplace/Beltrami operator) or in conventional PDE notation (using a Cartesian coordinate chart) as

${\displaystyle U_{tt}=U_{xx}}$

I propose to modify this page to correct this, if no-one objects.