Q.Calculate the modulation index for an FM wave where the maximum frequency deviation is 50 kHz and the modulating signal frequency is 4 kHz.

For a frequency-modulated wave the modulation index $m_f$ is simply the ratio of the peak frequency deviation to the frequency of the modulating signal, so it tells us how many times larger the frequency swing is than the message …

[!TLDR]

With a deviation of 50 kHz and a modulating frequency of 4 kHz, the FM modulation index is $m_f = 12.5$ (a pure number, no unit).

In frequency modulation the instantaneous carrier frequency shifts above and below its rest value by an amount called the frequency deviation $\Delta f$. The modulation index for FM compares this deviation with the frequency $f_m$ of the modulating (message) signal:

Here the maximum frequency deviation is $\Delta f = 50\ \text{kHz}$ and the modulating-signal frequency is $f_m = 4\ \text{kHz}$. Substituting, …