AC machine frequency: To generate an 800 Hz sine wave with a four-pole (P = 4) generator, at what rotational speed in revolutions per second (rps) must the rotor run?

Introduction / Context:
Synchronous generator frequency depends on the number of poles and mechanical speed. This relation is used to design alternators and set turbine speeds. Knowing how to back-calculate speed from a desired frequency is a practical skill.

Given Data / Assumptions:

• Desired electrical frequency f = 800 Hz.
• Number of poles P = 4.
• We assume synchronous operation and rps (revolutions per second).

Concept / Approach:

The standard relation is f = (P/2) * n, where n is speed in rps. Solve for n = f / (P/2).

Step-by-Step Solution:

Verification / Alternative check:

In rpm, multiply by 60: 400 rps * 60 = 24,000 rpm, consistent with high-frequency generation requirements.

Why Other Options Are Wrong:

200 rps would give 400 Hz with four poles. 800 rps would produce 1,600 Hz. 1,600 rps would produce 3,200 Hz. None match 800 Hz.

Common Pitfalls:

Using rpm in the formula without converting; forgetting to divide poles by 2 (pole pairs).

Final Answer:

400 rps