Suppose we have the 3D wave equation
$u_{tt} = 9 (u_{xx} + u_{yy} + u_{zz})$
$-\infty < x,y,z < \infty$ and $t > 0$.
Suppose that
$u(x,y,z,0) = f(x,y,z)$
$u_t(x,y,z,0) = g(x,y,z)$

Where $f(x,y,z)$ and $g(x,y,z)$ are zero outside the sphere of radius 6, and nonzero inside the sphere. At what time will an observer at position $(48,0,0)$ notice the disturbance, that is, what is the first time that $u(x,y,z,t)$ will be nonzero.
$t = {}$
help (numbers)