An arduino dial up modem?

Obviously there would be little use for one... but what about feasibility? Would a 56k (or slower) modem be possible?

Do you mean connecting a modem to an Arduino, or making an Arduino into a modem?

If you can find an old serial modem, that might work, although you might need an rs232 chip to interface with it at the right voltages, or maybe just some resistors & transistors for level conversion.

Nope, turning it into one....

In my country it is illegal to connect something home-made to a phone-line.
You would need extra hardware between the Arduino and the phone-line, and a sketch to act for example like an 14k4 modem. Perhaps the Arduino Due can do that if you put hundreds of hours work into it.
Buying a modem and using that is legal. You need an RS-232 adapter as PaulRB wrote. Sending modem commands from the Arduino is possible.

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