My 87 XJ is whining right now, really loud, little STP belt dressing and it stops.
I've had this happen many times on many Jeeps, solution has always been for me...replace the serpentine belt, that is IF the noise goes away w/ belt dressing.
I figured loosen the tension on the belt, nope, new belt always solves it.
The belt I have isn't awful; it's got some cracks here and there. Many might scream FOUL, but I ONLY buy the $30 Goodyear Gatorback belts now, they're twice as much, but they don't make noise a few months later like the half as much Kelly Springfield's(which goodyear makes).
If you try the belt dressing and it doesn't go away...then you've got a component issue, pump, alternator, or you've got a bearing or several in a pulley misbehaving. The A/C pulley, whether you have A/C or not tends to make some racket, in my experience.
As far as finding noises, go to a local harbor freight store, or online, they have an auto stethoscope for under $3.00, it has a long metal rod and I find I use it often now.
Just don't put it on and walk around with it on...it's loud.
Good luck!
Teron