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I am trying to clear my understanding of frequency bands.

When a particular wireless network standard like WiFi 6 claims operation in the $2.4$ GHz or $5$ GHz band, what do these values refer to? I am assuming they are the carrier center frequency of the transmitting device? The term band generally refers to a collection of frequencies. Does it mean the carrier center frequency of the devices may lie anywhere in $2.4 \pm \Delta$ GHz where $\Delta$ is a non-zero quantity?

The data rate of WiFi 6 is defined as a function of the channel bandwidth, e.g. 20 MHz, 40 MHz channels. How do we relate the channel bandwidth with the above discussion? Are they equal to $\Delta$ above? Also, I am assuming the channel bandwidth is the same quantity that appears in the shannon capacity expression $Rate = B \log(1 + SNR) $? Is that correct?

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what do these values refer to?

They are very human names. Neither 2.400 GHz nor 5.000 GHz are even part of the bands that they lend their name to.

By the way, this is very wikipedia-researchable.

I am assuming they are the carrier center frequency of the transmitting device?

No. They're referring to the unlicensed spectrum allocation that just got popularly known under the name.

In most of the world, the "2.4 GHz band" is from 2.401 GHz to 2.495 GHz, and the "5 GHz band" is from 5.150 GHz to 5.895 GHz.

How do we relate the channel bandwidth with the above discussion?

The 1, 10, 12, 20, 40, 80 or 160 MHz that the various technical standards for WiFi allow for channel bandwidths fall completely into the bands I describe one above.

I am assuming the channel bandwidth is the same quantity that appears in the shannon capacity expression R=B·log(1+SNR)? Is that correct?

No, but mostly because these channels are wide enough to be broadband, which means your SNR is not a constant over the whole bandwidth, and you need to look at how the interference, noise and frequency-selective channel manifests in individual parts of the channels, especially on the OFDM subcarriers.

Within the bandwidths that the channel is (approximately) constant in attenuation and noise power density is constant, that formula applies – but these bandwidths are much smaller than typical Wifi channel bandwidths.

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