Well, I unscrewed the plastic grille from my Lasko 3733 20" box fan and there it was, a permanent split phase motor with a 250 V 4.0 microfarad capacitor. (Horrible fan. I keep it in the kitchen because I can hang it from the ceiling in a jiffy to blow smoke out the window before it stinks up the house.)
How would you switch speeds with a shaded pole motor?