Why does the wave equation for a string apply to all types of waves?

[member 392791]

Hello,

I am studying wave mechanics and I managed to derive the linear wave equation with a string. Now I don't understand the significance of the equation or why I can use a string oscillating to make it general and apply to all sorts of waves

Edit:

this one

$$\frac{\partial^2 y}{\partial x^2}=\frac{1}{v^2} \frac{\partial^2 y}{\partial t^2}$$

 

[Studiot]

What equation did you derive, can you post it.?

 

[sukretep]

This may help you understanding, where this equation comes from:
http://amath.colorado.edu/courses/4380/2009fall/wave_equations.pdf