# How to calculate wave length

Given that 30GHz to 300GHz is considered mm wave spectrum which can be used for high-speed wireless communication such as 5G. My question is how to calculate the wavelength if we know the frequency? I suppose we have to know the wavespeed as $\lambda = v / f$ But do you know where to get wavespeed reference in telecommunications?

• … speed of light is practically the one reliable natural constant... – Marcus Müller Jun 28 '18 at 9:04

The "wavespeed" is the speed of light, which is 299,792,458 m/s if in free-space, or slowed by the root of the relative permittivity (dielectric constant for the material where the wave is propagating). So $v = c/\sqrt{\epsilon_r}$ and the formula for wavelength is $\lambda = c/(f\sqrt{\epsilon_r})$, where $c$ is the speed of light (299,792,458 m/s), $f$ is the frequency of the signal in Hz, and $\epsilon_r$ is the dielectric constant.
For example, a 30 GHz signal in air would have a wavelength of nearly 10 mm: $299,792,458/30\times10^{9}$.