Question: The monitor for my desktop hums/buzzes when a have a white background with a lot of black text maximized. I'm sure it would do it in other cases but this is the most obvious. I usually hear it when I am looking at a text file in an SSH client. 

What causes this? Is it clear that it is time for a new monitor?

I can provide details about my hardware if that will help.

It's a Dell 2001FP.

Answer: 
If its a CRT, try degaussing it (it'll be an option upon the on screen menu built into it usually). That sometimes used to help for me, anyhow.

If its an LCD, try lowering the brightness setting to 60% (which is usually easier on the eyes also) as they usually leave the shop cranked right up.
Obviously it's NOT a CRT, the model no that you kindly posted says FP at the end (mind you that is if I was too lazy to google it)... Pay attention folks. Aside from that, the thing is a tiny LCD - Buy a new decent sized one unless yer broke. Yes the buzz is indicative of an impending failure but it could be in five minutes or five years. It's Christmas time, spoil yerself and recycle this one properly.