Thanks Dave. I will look into that. The one thing I forgot to mention in my original post is the computer was doing this (playing the beeping song) before I erased the hard drive and started fresh. Even after I erased the hard drive the beeping continues at midnight. The computer did have Microsoft Office on it before I bought it thought so it's worth looking into regardless. Thanks for the reply.
Do you play DVD's on your system? Another user reported that if he left a DVD in his system and paused the movie his system would generate a series of beeps late at night. If you have a DVD in the system try removing it to see if the issue goes away.
Another person said they use Skype and the beeps were notifications as Skype contacts came online.
You may have to closely look at what you have installed on your system if neither of these provide clues. The Activity Monitor application (which can be found in the Applications/Utilities folder) can provide clues if you are willing to spend time looking at what processes are running and then using the 'Get Info' feature or googling any process names that are suspect to find out what they do.
You're welcome. That is even more puzzling that it was there before the HD wipe, but if you cloned it, it brought everything over. Sounds like you didn't clone, so it points more to Office being the common denominator.
To add to iCare's thought (or maybe this is what he meant), you could open Activity Monitor at 11:59 pm and sit there and watch it.