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The question is why 5 GHz has less coverage and more susceptible to attenuation in long range? How can we mathematically represent how many devices can be covered?

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why 5Ghz has less coverage and more susceptible to attenuation in long range?

It doesn't.

The limitation you might be thinking of is because as frequency increases, the receive antenna size gets naturally smaller and, as the antenna gets smaller it naturally picks up a smaller quantity of the radiated electromagnetic wave.

Think of a receive antenna as a fishing net; a low frequency requires a longer antenna and hence it has a bigger net aperture area whereas a higher frequency receive antenna is shorter and it's effective aperture is smaller.

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  • \$\begingroup\$ thank you very much! \$\endgroup\$
    – alfonso
    Jul 21, 2022 at 13:03
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    \$\begingroup\$ There are very important frequency-dependent attenuation effects, but they are nowhere near as simple as "more attenuation at higher frequencies". They depend on the absorbance/reflectance/transmittance/scattering spectra of the materials in the signal path. Biological tissue is a strong absorber at 2.4GHz, that's why that frequency is used by microwave ovens. \$\endgroup\$
    – Ben Voigt
    Jul 21, 2022 at 20:21

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