It sounds much like a tuning fork. When the furnace runs, you can hear this medium-pitch humming in any room that shares a wall with a cold air return. If you put your ear up against this wall, you can hear the resonance very loud and clearly.
The noise is only present around the cold air returns on the 1st and 2nd floor of the house. If you go in the basement and stand next to the furnace, you don't hear it at all.
Now that I think of it, I wonder if its the grills in front of the cold air returns that are "whistling" from the air flowing by and making this noise?
Failing that, are there products that you can use to line the inside of cold air returns to try to prevent resonance?
York Affinity series (93.2%, 60,000 BTU).