2003 GMC Sierra RPM noise over stereo speakers

I have made no changes to the stereo or electrical system, and they are all original manufacturer installed: I suddenly started hearing a high pitched noise over the speakers, that coincides with the RPMs. With the stereo off, I hear it for a second or two when I start the truck, then it is gone until I turn the stereo on.

I am told by an ameture mechanic that it is my alternator, and would like to just replace that and save the labor and diagnostic test charge I would pay a mechanic. Is this a fairly safe gamble?