(Solved): (1 point) The wave equation is a very famous differential equation given by \[ u_{t t}=a^{2} u_{x x ...

(1 point) The wave equation is a very famous differential equation given by \[ u_{t t}=a^{2} u_{x x} \] Show that \( u(x, t)=\sin (4 x) \sin (16 t) \) satisfies the wave equation: \( u_{x} \) \( u_{t t} \) \( a^{2}= \) so that \( u_{t t}=a^{2} u_{x x} \)