Physical significance of an equation of wave

[arpon]

We can mathematically derive the equation of wave,
$\frac{\partial^2 y}{\partial t^2} = v^2 \frac{\partial^2 y}{\partial x^2}$, where $v$ is the velocity of wave propagation.
Can we prove this equation physically (not just taking derivatives of the equation of wave, but making physical meaning in every steps)?

 

[ShayanJ]

You can find a derivation here.