Solve by using D'Alembert's solution with the even extensions of f(x) and g(x)

$\displaystyle \mu_{tt} = c^2\mu_{xx} $ where $\displaystyle 0\leq x <\infty$

$\displaystyle \mu(x,0) = f(x)$, $\displaystyle \mu_t(x,0) = g(x)$ where $\displaystyle 0\leq x <\infty$

$\displaystyle \mu_x(0,t) = 0$ where $\displaystyle t\ge 0$