Solve the following wave initial value problem by using the D'Alembert's formula:
$$\frac{\partial^2 u}{\partial t^2}−4\frac{\partial^2 u}{\partial x^2}= 0 \text{ with } u(0, x) = 1, \frac{\partial u}{\partial t}(0, x) = \cos(x)$$
We also need to plot three snapshots of the solution.
This is my solution using D'Alembert: $u(t,x) = 1 + \frac14[\sin(x+2t) - \sin (x-2t)]$.
I am confused on how I should plot $u(t,x)$. All values of $t$ which I pick as a snapshot look the same. I am not really sure what my professor means by "snapshot". Any ideas?