# Math Help - Solving infinite wave eq using Fourier Transforms

1. ## Solving infinite wave eq using Fourier Transforms

Solve the infinte wave equation
$\mu_{tt} = c^2\mu_{xx}$
$\mu(x,0) = f(x)$
$\mu_t(0,t) = g(x)$

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

2. Do what is suggested- write u as a Fourier transform, $u(x,t)= \frac{1}{2\pi}\int_{-\infty}^\infty A(t,s)e^{isx}dx$. Put that into the partial differential equation and derive an ordinary differential equation for A(s,t) in t with s as a parameter.