I am trying to find a general solution to the 1D-wave equation

Eq1:=diff(u(x,t),t$2)=diff(u(x,t),x$2);

pdsolve(Eq1,HINT=f(x)*g(t)); # Hinting pdsolve gives general solution using separation of variables

pdsolve({Eq1,u(x,0)=f(x),D[2](u)(x,0)=g(x)}); # without HINT and using intial conditions, I get travelling wave solution

pdsolve({Eq1,u(x,0)=f(x),D[2](u)(x,0)=g(x)},HINT=f(x)*g(t)); # Now when I try to use hint and ICs both, pdsolve return nothing.

I want to use separation of variables to find solution to the wave equation.

Any comment?

Thanks