معادله موج

${\displaystyle \left[\frac{\mathrm{\partial }}{\mathrm{\partial }t}-c\frac{\mathrm{\partial }}{\mathrm{\partial }x}\right]\left[\frac{\mathrm{\partial }}{\mathrm{\partial }t}+c\frac{\mathrm{\partial }}{\mathrm{\partial }x}\right]u=0}$

${\displaystyle \Downarrow }$

${\displaystyle \frac{\mathrm{\partial }u}{\mathrm{\partial }t}-c\frac{\mathrm{\partial }u}{\mathrm{\partial }x}=0\text{and}\frac{\mathrm{\partial }u}{\mathrm{\partial }t}+c\frac{\mathrm{\partial }u}{\mathrm{\partial }x}=0}$

${\displaystyle \frac{{\mathrm{\partial }}^{2}u}{\mathrm{\partial }{t}^2}-c^2\frac{{\mathrm{\partial }}^{2}u}{\mathrm{\partial }{x}^2}=0}$

${\displaystyle x+ct=\xi }$

${\displaystyle u_{\xi \eta }=\frac{{\mathrm{\partial }}^{2}u}{\mathrm{\partial }\xi \mathrm{\partial }\eta }=0}$

${\displaystyle u=f(\xi )+g(\eta )}$

${\displaystyle \omega =\frac{2\pi }{T}=2\pi f,k=\frac{2\pi }{\lambda },c=\frac{\lambda }{T}}$