I am studying for the General license exam and came across question G8B07 (as of April 2015, it will change at some point), asking the following:

What is the frequency deviation for a 12.21-MHz reactance-modulated oscillator in a 5-kHz deviation, 146.52-MHz FM-phone transmitter?

The answer is given as 416.7 Hz, but I looked and couldn’t find an explanation. Finally I found one here, sort of. After reading about how the FM phone modulation is done and puzzling a bit at the numbers it became clear.

To understand the question, you must understand that the reactance-modulated oscillator produces a carrier frequency of 12.21 MHz (as specified). With no input, this is multiplied by some circuits aptly called multipliers that result in the output frequency, given here as 146.52 MHz. Simply dividing 146.52/12.21 shows you that a multiplier of 12x is in effect in this question.

Now, what the question is asking (and this took me a while to figure out) is what change in modulation of the reactance-modulated oscillator will result in a 5 kHz deviation of the output? Since we know that whatever change happens in the oscillator is going to be multiplied 12x, we can divide the output deviation (5 kHz) by the multiplier (12) to get 416.7 Hz. In other words, a 416.7 Hz deviation in the reactance-modulated oscillator will be multiplied 12x to 5 kHz by the multipliers before being output.