Fundamental Frequency in FM

The fundamental (or sounding) frequency of an FM sound, is found by first representing the ratio of the carrier and modulator frequencies in reduced form:

$$\frac{f_c}{f_m} = \frac{N_1}{N_2}$$

($N_1$ and $N_2$ are integers with no common factors).

The fundamental frequency is then given by

$$f_0 = \frac{f_c}{N_1} = \frac{f_m}{N_2}.$$

Example: carrier frequency $f_c=10$ and modulator frequency $f_m = 5$ yields the ratio in reduced form:

$$\frac{f_c}{f_m} = \frac{10}{5} = \frac{2}{1} = \frac{N_1}{N_2},$$

and a fundamental frequency of

$$f_0 = \frac{f_c}{N_1} = \frac{10}{2} = \frac{f_m}{N_2} = \frac{5}{1} = 5.$$