I have the PDE:
$u_{tt}=u_{xx},\quad 0<x<1,\,0<t<\infty \\ u(0,t)=0 \\ u(1,t)=\sin\,t \\ u(x,0)=u_t(x,0)=0,\quad 0<x<1$
When i used the D'Alembert formula i got $0$ because $f(x)$ and $g(x)$ (Initial function) is $0$ Am i wrong? But it's weird if the solution $u(x,t)=0$