Unraveling the Wave Equation: Exploring its Origins

[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.

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