An induction motor's synchronous speed Ns is given as:
Ns = frequency * 120 / number of poles
This formula is independent of the voltage applied to the windings.
On the other hand, I know from basic theory that if the voltage across a solenoid is increased its magnetic flux will increase. And more magnetic flux will create more force on a current carrying wire.
Would the speed of the induction motor's rotor change with delta or star connection? And is there a formula explicitly shows such dependency between stator winding voltage(delta or star) and rotor speed? Would a three phase fan motor rotate faster if connected delta instead of star?