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?

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    $\begingroup$ … speed of light is practically the one reliable natural constant... $\endgroup$ – 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.

Example dielectric constants:

  • Air at 0°C: 1.000594
  • Air at 20°C: 1.000528
  • Glass: 5 to 10
  • Paper: 3.85
  • Silicon: 11.68

For example, a 30 GHz signal in air would have a wavelength of nearly 10 mm: $ 299,792,458/30\times10^{9}$.


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