Synchronous Speed:
The synchronous speed of an induction motor is given by the formula:

Synchronous speed = (120 * Frequency) / Number of poles

Given that the frequency is 50Hz and the number of poles is 4, we can substitute these values into the formula to find the synchronous speed:

Synchronous speed = (120 * 50) / 4
= 1500 RPM

Therefore, the synchronous speed of the motor is 1500 RPM.

Rotor Speed at 4% Slip:
The speed at which the rotor of an induction motor rotates is given by the formula:

Rotor speed = (1 - Slip) * Synchronous speed

Given that the slip is 4% and the synchronous speed is 1500 RPM, we can substitute these values into the formula to find the rotor speed:

Rotor speed = (1 - 0.04) * 1500
= 0.96 * 1500
= 1440 RPM

Therefore, when the slip is 4%, the rotor speed of the motor is 1440 RPM.

Rotor Frequency at 600 RPM:
The frequency at which the rotor of an induction motor operates is proportional to its speed. We can use the formula:

Rotor frequency = (Rotor speed * Number of poles) / 120

Given that the rotor speed is 600 RPM and the number of poles is 4, we can substitute these values into the formula to find the rotor frequency:

Rotor frequency = (600 * 4) / 120
= 20 Hz

Therefore, when the motor runs at 600 RPM, the rotor frequency is 20 Hz.

In summary, the synchronous speed of a 3-φ 4 pole induction motor supplied from a 3φ 50Hz AC supply is 1500 RPM. When the slip is 4%, the rotor speed is 1440 RPM. When the motor runs at 600 RPM, the rotor frequency is 20 Hz.