Hum or Roar from Engine

I have a '96 Chev. Tahoe with the 5.7 cu.in. with 102,000 miles. Yesterday I drove it to the supermarket.. No noise, just same old normal engine noise. This morning I started it to go to the gold course, and it had this hum or low roar coming from the engine. I raised the hood and it sounded like it was coming from the rear of the engine. I had a new transmission installed at 100,000 miles, some 6 months ago. I figured it was the trammy. Then I started thinking, it may be something else.
So I removed the serpentine belt, and started the engine.. No noise...
Now that I have located the trouble. either the "tensioner pulley, alternator, or water pump, or air compressor" is bad.

So I made a trip to the auto supply store and bought a pulley ($15.00) for the tensioner arm, and a serpentine belt. Installed both.. Noise is still there. So I removed the alternator, and will take it to the auto supply store tomorrow for testing..

It may be the water pump, but I see no leak coming from that area, and I don;t think it is the air compressor pulley, as I turned on the air conditioner and no added noise.

I installed a new alternator in 1999, and this may be the culprit.

Anyone have have a better idea where the noise in coming from?

Thank you for the wonderful help here. You can always depend on expert knowledge.

Being that over the past fifty three years I probably saved myself about $50,000 dollars by working on my own autos, this little problem with the Tahoe was minor.

Bought a new Delco-Remy 105 amp alternator this morning, and installed it in about twenty minutes. The problem solved.

My neighbor ask me why I didn't take it to the dealer for the repairs. I told him a person that can fly US Navy fighter jets and make 2027 aircraft carrier landings, surely can use a wrench to remove a few bolts.
Besides, I know anything that man can but together, man can take apart.