Solve the infinte wave equation

$\displaystyle \mu_{tt} = c^2\mu_{xx} $

$\displaystyle \mu(x,0) = f(x)$

$\displaystyle \mu_t(0,t) = g(x)$

using Fourier Transforms and show the solution reduces to the D'Alembert Solution.

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- Mar 22nd 2009, 03:26 PMflamingSolving infinite wave eq using Fourier Transforms
Solve the infinte wave equation

$\displaystyle \mu_{tt} = c^2\mu_{xx} $

$\displaystyle \mu(x,0) = f(x)$

$\displaystyle \mu_t(0,t) = g(x)$

using Fourier Transforms and show the solution reduces to the D'Alembert Solution. - Mar 23rd 2009, 07:35 AMHallsofIvy
Do what is suggested- write u as a Fourier transform, $\displaystyle u(x,t)= \frac{1}{2\pi}\int_{-\infty}^\infty A(t,s)e^{isx}dx$. Put that into the partial differential equation and derive an ordinary differential equation for A(s,t) in t with s as a parameter.