Is the fan a mechanical fan in the Tahoes? If so then it sounds like your fan clutch may be going bad. That would be my guess as anyone else who has ever expalined that noise to me had that issue including myself (on an old truck). When the truck is cold the fan should barley spin, but if it seems fully engaged when cool then that is a problem. It will not hurt anything but it will be loud and cost you gas mileage.
Now if the noise does not change with the RPMs of the engine then it would be something else.