What Are the Origins of the Wave Equation?

[coki2000]

Hi,
Why the wave equation is
\frac{\partial^2 u}{\partial^2 x}=c^2\nabla^2 u?
Where does it come from?Thanks.

 

[Integral]

Hi,
Why the wave equation is
\frac{\partial^2 u}{\partial^2 x}=c^2\nabla^2 u?
Where does it come from?Thanks.

For me to consider your relationship the wave equation I would have to change it to:

\frac{\partial^2 u}{\partial^2 t}=c^2\nabla^2 u

The wave equation is probabley derived in every intro to PDE textbook.

https://www.amazon.com/dp/0486688895/?tag=pfamazon01-20