Okay, a whine is generally from the alternator and can, in some instances, indicate an alternator that's starting to "go".
The place to start with these type of radio noise problems is with checking your grounds. Particularly important with these trucks (I have a '99 GMC too) is the block to frame strap located on the passenger side rear of the engine. Also important is the frame to body strap there, and the pigtail that sometimes comes off the negative battery terminal and goes to the fender. Check all of those for broken, loose or corroded connections. Clean, tighten and replace as needed. Don't neglect the usual negative cable to the block. Make sure that's clean & tight too.
If you still have the whine after that I'd suggest having the alternator checked by a good shop.
You can also run the leads for the CB direct to the battery (preferred method with any two-way radio gear) using good wire (ie: not speaker wire or an old extension cord) that's properly sized for the current and properly spliced (preferably soldered) to the cord on the radio.
If that all doesn't solve the problem I'd suggest a ferrite bead or a torroid added to the power lead.