Jim and Rob -
It's hard to say that one item makes the woo-woo sounds exactly, it's probably a combination of things.
Motors have something to do with it. There have been GE, Delco, and Emerson motors in BD washers over the years. I always thought the later GE motors that were square (unserviceable) made a higher pitch just in operating than the Emersons.
Most of the 24-inch and 29-inch standard cap machines had split-phase motors (which were often GE), whereas the large cap machines had capacitor start motors which were usually Emerson - at least speaking to later production. The split-phase motors start a little bit more slowly, and they give off some more pleasing sounds during start up than the capacitor start motors which spring to life instantly.
The belt itself is the biggest contributor to the woo-ing, and the worn state of the belt can slow it down as it seats further into the pulleys with wear. I believe that with wear, the machine's pitch changes. However, I have four belt-drives here, some with original belts and some not, that emit four distinctly different woo-woos and they are essentially the same mechanically.
Since we know that the 'quiet-pak' machines can be largely almost silent, things like pumps and transmissions don't contribute much to the sounds. The basket drive pulley can make a lot of unpleasant noise, and the pump does make some suctions sounds when operating, especially in drain.
Mostly it's the belt itself and this can vary from one belt to the next. Belts were revised over the years. Randy's machine has a 95405 belt, which is the current number for the big non-quiet belt and was revised to be more flexible and less prone to breakage than the earlier belts. I am sure that a change in materials altered the belt sounds a little bit. The 95405 belt has been standard equipment since the mid 60s, though I don't know when exactly that it replaced the previous version.
As to 24-inch machines, I have always figured that cabinet geometry contributed to the higher pitch on them, and I have noticed this myself.
Sorry for a non-definitive answer!
Gordon