How does a signal travel down a telephone wire?
Over several decades of time analog telephony modem technology has evolved quite a bit. To understand the basics it is essential to understand Frequency Shift Keying, (in my opinion) the mother of all modulation schemes for digital signals.

Essentially what is happening is that a byte is broken up into separate bits, which will be sent one after the other. Next a couple of extra bits are introduced to simplify error detection and synchronization to the signal. If you miss a single bit, you don't want to corrupt the rest of the data stream too.

Unfortunately a telephone line cannot transmit logic levels on its own, the frequency band that it allows is too small (I believe 300-4000Hz) and thus you need a way to change the bits into something that can be transmitted across the telephone line => tones. This is just what FSK does, it changes a logic 0 into a tone of a certain frequency and a logic 1 into a tone of a different frequency.

For example a simple modulation scheme would work like this:


Serialize the bits at a given rate, say 1200 bits per second. This was once a very common bitrate.
For every 0 insert a single sine wave at 1200Hz
For every 1 insert two subsequent sine waves at 2400Hz.


Notice how 1200Hz and 2400Hz are right in the supported bandwidth of the telephone line (300-4000Hz).



At the receiving end it is you do the reverse, if you detect a 1200Hz wave, you shift out a 0 and if you detect two 2400Hz wave, you shift out a 1.

Now you can pick two other frequencies for the communication in the other direction.

To increase bitrate there are many options. You can use multiple frequencies, multiple amplitudes and some schemes can even synchronize on the clock noise of the remote modem.