To expand on this just a bit, I had some time today as my 2002 A4 3.0 was doing the same three beeps...I assumed it was the same deal...I pulled the passenger side luggage compartment interior panel (which was a job in and of itself-must pull rear trunk plastic guard off (4 circlips and two nuts and disconnect the trunk light) then pulled the tiedowns (two torx bolts ea.) then pulled the panel (3 circlips towards the aft end, 1 metal tab on the top (you can see this without having the panel pulled unlike the circlips which are behind the panel-I used an interior pry tool for all circlips being very careful-you can damage the clips or holders if you don't know how to pry on them) and lastly don't forget the small plastic clip on the top center of the panel (get your tool under the small tab and pull out until the whole deal comes out-see pic)
I also found that you need to put the rear seat down and gently pull the panel out from behind the interior-I didn't pull mine all the way out from under the seat as I found I could get to the parts needed without pulling the panel all the way out. (Don't forget to disconnet the wire to the 12vDC outlet)
Once behind the panel I found lots of cool things...the manual gas filler panel release(accessable w/out pulling the panel)...I knew it was somewhere back there
..., the auto lock mechanism, what I think is the amp for the Bose sterio system, and lastly the alarm. A word of caution, when you disconect it sounds...not for long though, and when I reconnected it to get it to turn off, it got louder...a lot louder. it does shut off after a few seconds (I don't know if that is a function of the battery going or normal ops) you disconnect it by getting a thumbnail under the tab and pulling up on the whole connector, it pops right off.
So I'm stuck now...the whole alarm piece is sealed and since it says "Ni-MH" (Nickel Metal Hydride) on it I'm guessing this is the battery that needs replaced...I'm going to call the dealer and see what the part costs but I'd really like to confirm that this will fix the 3 beep issue first...