$3.$ A three$-$phase induction motor rotates at approximately $745$ rpm in no$-$load condition and at $710$ rpm under full load, being supplied by a three$-$phase current of $50$ Hz $.$

a$)$ How many poles does the motor have and what is the synchronous speed?

b$)$ What is the frequency of the rotor voltage at full load?

c$)$ At full load, what are the relative speeds:

$(1)$ of the rotor field relative to the rotor?

$(2)$ of the rotor field relative to the stator?

$(3)$ of the rotor field relative to the stator field?