The sound is not a byproduct, It is the direct transmission, but instead of being human-readable, its machine-readable. Its actually a clever hack to use the already existing Telephone infrastructure, in a time before fiber-optic cables everywhere.
Now for what’s actually being transmitted:
The first sounds were actually the dial tone and the phonenumber, to which the answering modem would respond with a dedicated Tone as well.
After that, both modems communicate their capabilities and settle on terms of the communication.
Now that the connection is established, data from the computer in the form of zeros and ones are sent to the modem, which translates it into sound, which can get translated back into binary by the other modem.
If you want to know what exactly these packets are, you can look at one example – the http handshake – which would be used to connect to a website.
https://developer.mozilla.org/en-US/docs/Web/HTTP/Session
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