I am shocked that no one has even mentioned the possibility of a PC Speaker yet. DUH!!

Try muting your computer (removing the PC Speaker). If that doesn't work, it could be a feature with the monitor. What model is it? Look for an FAQ. Your problem will probably be answered there.

If the aforementioned do not work, try solving this yourself. What else does it do when the beeping occurs (E.g. Automatic Degaussing)? Maybe a cord is loose. Maybe it just needs to be thrown out a second- or third-story window.

Consider these.

-ThO