Bicycle Mechanics - Earl Grey anyone?

So I picked up (CL curb-alert!) this hybrid/comfort Giant Farrago (http://www.bikepedia.com/QuickBike/BikeSpecs.aspx?Year=1998&Brand=Giant&Model=Farrago%20%2801%29&Type=bike), and I got it running OK for my wife, but there's this sound coming from the rear hub that's like a teakettle. Once in a while it will stop, but mostly its just droning on with this high-pitched whine, sometimes it changes pitch cyclically with the wheel rotation (like a little fire engine siren: wee-ooo wee-ooo wee-ooo...)

What could possibly make a wheel sound like that, and what can I do about it?

The jockey wheels in the rear derailleur may need grease ...

They may and probably do, but this noise is unaffected by pedaling or coasting. I have pinpointed the noise to the rear hub by ear, from spinning the rear wheel in the air. And this noise is much more like a whistling than a squeaking.

Some hubs coime with a large rubber 'cap' thintended to seal out contaminants, and when these are dry they can cause a persistent squeaking noise. If her bike has a rubber dust cap, try putting a drop of oil between the hub body and the seal.

Nice -- I like that suggestion because I can attempt it without having to take the hub apart, bcos I got no tools for that! I'll try it tonight, and give an update.

The scientific way to do this would be to move your wheel on your wife's bike and try it out. I never trust my ability to locate squeaks and tea-kettle sounds.

That's a good idea too, but I'm not sure how well it would work, I've got a road bike with 700Cx23, hers is a (29er?) hybrid with 700Cx38, besides I have a 7-speed cassette and I believe she's got 8. But probably I could jam that wheel in there and get the chain to sit on one of the gears.

Even easier, I could double-check that it's the hub by just taking her wheel out and see if the sound persists just spinning it in my hands. I'll try that too. Should make it easier to try to drop oil in if the frame is not in the way.