Fundamental Frequency in FM

In determining the fundamental frequency of an FM sound, first represent the ratio of the carrier and modulator frequencies as a reduced fraction,

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

where $N_1$ 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: a carrier frequency $f_c = 220$ and modulator frequency $f_m = 110$ yields the ratio of

$$\frac{f_c}{f_m} = \frac{220}{110} = \frac{2}{1} = \frac{N_1}{N_2}.$$

and a fundamental frequency of

$$f_0 = \frac{220}{2} = \frac{110}{1} = 110.$$

Likewise the ratio of $f_c = 900$ to $f_m = 600$ is 3:2 and the fundamental frequency is given by

$$f_0 = \frac{900}{3} = \frac{600}{2} = 300.$$