When a 60 Hz sinusoidal voltage is applied to the input of a half-wave rectifier what is the output frequency?

The output frequency of the half-wave rectifier will be 60 Hz if the input is a 60 Hz sine wave.

One cycle of the input will include the positive going and the negative going portions of the sine wave. The output will have either the positive going or negative going half of the input wave, and will have no output during the other half of the input sine wave when the diode is reverse biased. What that output will look like on an oscilloscope is half a wave and then a "flat spot" where there is no output (owing to the diode being reversed biased). Let's keep going.

The frequency of a signal is the number of cycles of the signal per second. Further, we know that in a waveform, one cycle occurs when the wave goes through all of the changes it must go through to, shall we say, get back to where it started. In the half-wave output, the signal goes through half of the input wave, and then the voltage sits at zero. That means that one output cycle consists of that voltage excursion, and that period during which the diode is back biased. So the time for one complete cycle of the output is the same as the time for one complete cycle of the input. Thus, a 60 Hz input signal (that sine wave) will give us a half-wave rectified 60 Hz output signal.