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owl writes:

https://www.10stripe.com/articles/why-is-56k-the-fastest-dialup-modem-speed.php

If you've ever had dialup internet service, or still do, or just know someone that does, you have probably heard terms like "56k modem". "56k" has become almost synonymous with dialup Internet access. But it's such an arbitrary number. It's not divisible by ten, it's not a power of two... so why was it chosen as the fastest dialup speed? For the answer, we will have to travel back in time quite a while.

Our visitors from Google should be warned that this is not a "stripped down" explanation; it is intended for relatively technical readers. But if you really want to know where this magic number comes from, you need to understand some of the technical background. As we shall see, "56k" was not just pulled out of a hat.

[...] Anyone that has ever used a dialup modem knows full well that they don't actually get to connect at that speed, though. And that their connection speed varies each time they dial in. There are two factors at work here.

The first is the FCC. If you are in the United States, the FCC places a restriction on the power output of devices connected to the phone network. The result is that you will never be able to connect at a speed faster than 53.3 kbit/s.

The second is the overall complexity of the phone network. 56 kbit/s (or 53.3 kbit/s) requires very good operating conditions, as it is really operating beyond the paramaters of what the phone network is required to be capable of. Operating at these speeds requires that there only be one ADC between the user and their ISP (which is not guaranteed to be true, but typically is), and that the copper wiring in the user's "local loop" have very good electrical properties. Part of the dialup process that is used to initiate a connection is an evaluation of the overall quality of the connection; if it is determined to be lacking, the modem will automatically drop down to a lower data rate.

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