Final answer:
The synchronous speed of the motor would be 1440 RPM with a 48 hertz AC voltage.
Step-by-step explanation:
A synchronous motor is designed to rotate at a specific speed, known as the synchronous speed, which is determined by the frequency of the AC voltage applied to it and the number of poles in the motor. The synchronous speed (Ns) of a motor can be calculated using the formula: Ns = (120 x f) / P, where f is the frequency in hertz and P is the number of poles per phase.
In this case, the AC voltage applied to the motor has a frequency of 48 hertz and the motor has four poles per phase. Plugging these values into the formula, we can calculate the synchronous speed as follows:
Ns = (120 x 48) / 4 = 1440 RPM (revolutions per minute)
Therefore, the synchronous speed of the motor with this voltage applied would be 1440 RPM.