Ah...an induction motor cannot rotate at synchronous speed. If it doesn't slip, it doesn't induce field currents. A, say, 2 pole 60 hz induction motor can't rotate at 3,600 rpm. With only parasitic load it might turn close to that--windage, bearing drag, fan.
Small universal AC motors (the ones with brushes) have their speed regulated by the current in the armature and the magnetic field around the armature. This, of course, relates to voltage.
I've operated dual voltage 400v 50 hz 3 phase and 460v 60hz 3 phase motors that were built and labeled for that. Don't try it unless it is on the nameplate.
2-phase power? The generators at Niagara Falls' 1895 power station were 2-phase. It might still be in some antique buildings. (AC power is represented by a sine curve. Draw another sine curve 90° out of phase alongside the first curve and you have represented 2-phase power. 3 sine curves 120° apart represents 3-phase power.) Everything for a very long time has been single phase or 3-phase.