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I understand that my internet speed over Wi-Fi will deteriorate over distance , especially through walls. My question is, will speeds drop to a set value, or will it drop as a percentage of the original.

for example. If I stand right next to my router, i can get 100mbps (my max internet speed). When I stand in my office (a few rooms away). I get 20mbps.

So my question is, if I were to increase the internet speed at the source, i.e. to 200mbps by upping my subscription to my internet provider, will I still get 20mbps in my office , or will it increase to something like 40mbps.

Note: I know that I can get better speeds in my office by running a cable and installing an AP. I'm looking for an explanation specific to my question

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Most likely, your office link will stay the same.

It's not a matter of the Internet signals deteriorates by a factor of x which might be deducted from the analog world.

Rather, the network path consists of multiple links (ISP↔router via DSL or fiber, router↔WAP via Ethernet, WAP↔client via Wifi) and the overall performance is limited by the weakest=slowest link - the bottleneck. Since the Wifi link isn't changed, its performance doesn't improve.

You could improve the link by moving the WAP closer to the client, using a WAP with a better directional capability, or by simply running a cable.

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