Show that the general solution of the wave equation

$$\frac{\partial^{2} y}{\partial t^{2}}=c^{2} \frac{\partial^{2} y}{\partial x^{2}}$$

where $c$ is a constant, is

$$y=f(x+c t)+g(x-c t),$$

where $f$ and $g$ are twice differentiable functions. Briefly discuss the physical interpretation of this solution.

Calculate $y(x, t)$ subject to the initial conditions

$$y(x, 0)=0 \quad \text { and } \quad \frac{\partial y}{\partial t}(x, 0)=\psi(x)$$