So I'm thinking of increasing my Internet connection by 40 Mbit/s, also doubling it. This is because in the furthest corners in my apartment I have 1 Mbit/s. So when I increase will I get 41 Mbit/s or 2 Mbit/s in those areas?
If you increase your WAN speed, your WiFi will stay the same bottleneck it is now. To improve speed "in the furthest corners" you need to improve WiFi connectivity first.
Your water tap is somewhat clogged. It won't matter if you double the cross section of the pipe to the waterworks, until you fix the tap. Similar situation.
Just for clarity there are two links / connections here, not one:
- From your ISP to your house.
- It has bandwidth of 40 Mbit/s
- From your router to the WiFi device(s) "in the furthest corners of your apartment"
- It has bandwidth of 1 Mbit/s
The bottleneck here is link #2.
Doubling the speed of link #1 will not affect link #2 at all, unless you reduce it to less than the speed of link #2 (at which point, link #1 will become the bottleneck).
Think of it like pipes (as per Kamil's answer), or roads...
A highway / motorway might have 3 lanes in each direction, while a back road will have one lane for both directions with passing places. You can't get more cars down that back road by making the motorway leading up to it larger.
In this situation you want to look into moving your WiFi access point (often built into the router), or if that isn't possible, look into getting WiFi range extenders. Another option could be to purchase high gain antenna(s), but please check that the router or device has removable antennas first.
You could also look into using Powerline adapters and a WiFi access point to provide a more localised service at the far end of your appartment.
If the 40 Mbit/s connection is adequate for everything you need, there is no reason to upgrade that link - it won't help with this problem. If you have been advised that it will help, then unfortunately that advice was incorrect.
Headline (deceptive, please update) answer : Yes
Qualified answer, no.
Regardless of the "backwater bandwidth" endured in the farthest corners of the house, the "consumable" bandwidth will actually double. At the modem or MAC you have the potential to see 40Mb/s down. Further, peer to peer on the house network you should be seeing 100Mb/s for Cat5e and 1Gb/s on Cat6. If you have to share any broadcast domain (including WiFi) that will obviously degrade performance.
But no, if you are getting 1Mb/s now, that is a limit.
For Wifi, run ethernet to a second AP, and use high gain antennas, get rid of, and do not use repeaters, they are half duplex and extend range at a terrible cost to bandwidth. Find the clearest channel you can, your neighbours may be swamping you.
If these are workstations, consider WiFi to ethernet bridges, and place antennas at ceiling level.
If you can't do this,or can't run cable at a minimum use an external high gain antenna and place it/them high up.
To answer your question, it increases mostly rationally (the latter) - if you imagine it as waves bouncing around your house, an increase by 20% just means that the signal is 20% stronger to get through walls, etc. What it is near the router means nothing, since it still has to travel through the air!
However, this is not perfect either, as when it travels we can't imagine that no energy is absorbed by the surroundings, but the absorption doesn't increase rationally. So I'd estimate it would go from around 1mbps to 1.8mbps, although it may vary.
It may just be wiser to consider wireless boosters; they're only $20-30 (depending on what router and ISP you use) or buying a better router. Increasing what comes out of the socket may be useful to some extent, but it's a waste of money compared to buying a stronger router, which will not increase your maximum internet speed (i.e when you are next to the router, the speed will be the same as before), but it will extend the range in which the signal is usable. TPLink makes good ones for $70; they generally have 4+ 3-axis flexible antennas, meaning you can push the signal in multiple directions.
Hope this helped.