As in synchronous motor, rotor and stator are synced with each other and the rotor rotates with the same speed as the rate of change in rotating flux in the stator.
Thus, the speed of a synchronous motor can be given using a relation:
In this equation, P is the number of poles of stator and f is the frequency of the voltage signal applied for excitation of the stator.
From relation, it is clear that the speed of stator Ns is inversely proportional to the number of poles of winding. So increasing the number of poles will reduce the speed of the motor. While decreasing poles will result in increasing speed.
Similarly, speed is directly proportional to the frequency of applied voltage. More frequency will mean faster switching of flux due to reduction of time taken by the signal to complete one cycle. Therefore, more flux will result in larger speed of the motor.
Thus, for a 50 Hz signal the value of the speed of the motor for two poles winding will be 3000 revolutions per minute (r.p.m). It will drop to 1500 r.p.m at the same frequency value for four poles winding motor. Similarly, it will be only 500 r.p.m for a motor with stator winding of 12 poles.