The 1D wave equation for P-waves is:
\(\frac{\partial^2 u_{1}}{\partial t^2}=\alpha^{2}\frac{\partial^2 u_{1}}{\partial x_{1}^2}\), where alpha is the P-wave velocity.
Show that the function
\(u_{1}(x_{1},t)=Asin[\omega t-kx_{1}]\)
is a solution for the wave equation, where A is the maximum amplitude and omega is the angular frequency.