to determining if it's the water pump or alternator making the whiny sound, take a metal rod or 3/8 drive extension/s, long enough so your face isn't getting slapped by the fan or what ever to make a stethoscope to get sound to travel through. Be careful to not get it into any moving parts. With engine running, take the metal rod and carefully put it on the alternator housing and put the other end up next to your ear, touching just before the ear opening, listen to the sound being transferred. Now carefully take the rod and put it close to the water pump housing and listen to the sound. Which one sounds the loudest ?
if it was your water pump, the bushing is on it's way out and you should see some weeping of anti-freeze coming out on the ground.
if it's the alternator, sometimes all you need to do is open it up, ( hope you know how to) and put a little grease on the bearings.
hope this helps, report back with your findings.