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.
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.
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.