So my girlfriends Toyota RAV4 (2005) is making a medium pitched whirring noise from the passenger side of the engine compartment. (Same area where the serpentine belt and the alternator and all those goods are located.) The battery warning light is on, solid. I have not had a chance to take my DMM and check voltage but I suspect this is going to be a bad alternator since it is a noise consistent with the RPM of the vehicle and visual inspection of the belt is that it is still in one piece, not frayed, flexible, etc. I didn’t rev the engine because I didnt want to freak her (the gf) out. My plan is to test voltage before she does anything rash like take it to the dealership which she is already planning on doing but the noise concerns me since noises tend to come from things that move which is probably an indication of some sort of mechanical failure and that tends to cost money. Luckily it’s her car. Any thoughts much appreciated. Thanks!!! 
A length of heater hose, paying close attention to extremities that can get damaged by moving parts can be a helpful tool. Could be 2 problems unrelated. Get a free battery test from a local cooperating auto parts store, Check the voltages while charging ie engine running, then with engine off, though iv you have a gauge in the cluster that is easier. Depending on the dealership I would not consider it a bad move out of the gate automatically.
Battery light is on? And u think dealer might say alt is bad? Nah, u got a bad gauge cluster. U need a new dash.
My vote is for a bad alternator. As @Barkydog says, a short length of hose used as a stethoscope can help zero in on the source of the whirring noise. The voltage reading at the battery when the engine is running will be helpful.
Thanks for the replies! I will try the heater hose idea and report back after I have a chance to test the voltages.
How about checking belt tension first . . . ?!
With insufficient belt tension, you can’t expect too much from the alternator . . . 
I have a feeling it’s going to be the alternator in the end
But check that belt first
By the way, how old is that battery?
Why would you take a 10 year old car to the dealer? Any competent independent shop can fix this and is usually much cheaper than the dealer? This is a good opportunity to build a relationship with a good mechanic that is convenient to where you live.
This is another vote for a bad alternator. I just had one go bad on my truck and the rear bearing was showing through the case. It made no noise until it seized up with that awful “whirring” noise.
Battery light is on? And u think dealer might say alt is bad? Nah, u got a bad gauge cluster. U need a new dash.
Attempted humor?
“Battery light is on? And u think dealer might say alt is bad? Nah, u got a bad gauge cluster. U need a new dash.”
Humor? Hardly…that’s how a lot of dealers talk. They are in the business of making money…not car repair.
Check amount of ac v from alt. Should be in low tenths.
Do not overlook the battery load test as advised by Barkydog, a battery can develop an internal short and that can ruin a good alternator. I do think it will be a bad alternator, but before putting in a new one, get the battery load tested just to be on the safe side.