What is the only way to vary the output frequency of a rotor?

Varying the output frequency of a rotor can only be effectively achieved by adjusting the rotor speed. This relationship stems from the basic principles of electromagnetic induction and the operational characteristics of motors and generators, where frequency is directly related to the speed at which the rotor moves.

When the rotor speed increases, the frequency of the alternating current (AC) generated also increases, and similarly, a decrease in rotor speed results in a decrease in output frequency. This direct correlation is pivotal in applications like synchronous motors, where maintaining a specific frequency is essential for system performance.

The other options—changing the rotor's material, modifying stator connections, and altering the power input—do not provide a means to directly control frequency. While these factors can influence motor performance, efficiency, or characteristics, they do not fundamentally change the frequency output which is dictated by the speed of the rotor. Essentially, controlling rotor speed remains the primary and straightforward method to achieve variations in output frequency.