If you've ever used an actual Atari 8-bit computer with either a cassette or disk drive, you would have noticed that it made a variety of "beeping" noises while accessing the devices. Specifically, loading a cassette made a "cluuug" sound repeatedly with small pauses and the disk drives made "bee-dee-bee-dee-bee-dee" type sounds while reading and "plut-a-plut-a-plut-a" type sounds while writing.
While it was good to have an audio indication as to what was going on, I never understood why the machine made the noise. It certainly wasn't the sound of the data coming off the device (since that'd presumably sound more like white noise), but the devices weren't as slow as (say) the Commodore 64 & 1541 where you could go have a cup of coffee in the other room and listen for when your game was finished loading.
What was the reason?
I don't think I've used an Atari emulator which reproduces these noises - I'd assume it is because the authors didn't see the need.
As a side note, I seem to recall that different drive manufacturers (e.g. Atari VS Rana) may have had different sounds. Is my memory correct? If so, that would say something more about the sound being a product of the device rather than the Atari.
UPDATE 2017-01-18: There are two answers to this question which suggest "the sound of the data" either leaking through or otherwise. I recently brought my Atari 410 deck back to life and have been loading converted CAS-to-WAV files via an iPod and a headphone jack-to-cassette adapter.
My memory from years ago was that you only heard a mix of silence and the "clooooooog" sound when the tape was being loaded. I was a bit surprised that instead of silence I was hearing the high pitched screech of the cassette data while loading tapes with the iPod, but it dawned on me that its because these converted WAV files are being played in stereo. So instead of data on track 1 and a silent track 2, I'm hearing the data screech from the stereo conversion since the normally silent other track is passed through to the TV speakers (as it would have been used for loading music, instructions, etc).
So what does this mean? You normally did NOT hear the data screech of a cassette, only the "cluuuuug" sound. When does that sound get made? If we assume the carrier signal (or '0') is 5327Hz and the "mark" (or '1') is 3995Hz, the sound only gets made when it detects a data stream (i.e. a mixture of 0's and 1's), though I suspect it is only making the sound when it detects a "mark" but perhaps rounded off a bit since it isn't as fine grained as I hear from the data stream.
All that being said, it doesn't answer the disk drive noise side of the question. Perhaps it is just simply more of "data packet being received over SIO" indication sound?