# Long wavelength limit

The physical criterion is that ${\displaystyle \lambda >>a}$, where ${\displaystyle a}$ is the size of the system. The following statements are all equivalent:
• ${\displaystyle \lambda >>a}$
• ${\displaystyle ka<<1}$, where ${\displaystyle k}$ is the wave vector
• ${\displaystyle {\frac {\omega }{c}}a<<1}$, where ${\displaystyle \omega }$ is the angular frequency, ${\displaystyle c}$ is the propagation speed of waves.