How to use D'Alembert formula for Dirichlet boundary conditions on a finite interval?

Question

I have a wave equation to solve that I am not sure how to do. I know how to solve this using D'Alembert's formula without boundary conditions but I do not know how to solve it for Dirichlet boundary conditions. \begin{equation}u_{t t}- u_{x x}=0, \quad u(x, t_{0})=f(x), \quad u_{t}(x, t_{0})=g(x), \quad u(0,t)=u(1,t)=0 , \quad x \in (0,1) \quad t \in (t_{0},\infty)\end{equation}