{c}
{title2=$\beta=\Delta f/f_m$}

For a message consisting of a single <sinusoid> with <frequency> $f_m>0$, the FM modulation index is $\beta=\Delta f/f_m$. It is dimensionless and equals the peak <wave phase> excursion in <radians> in the chosen sine-phase convention. Keeping $\Delta f=5\,\mathrm{Hz}$ while changing $f_m$ from $1$ to $2\,\mathrm{Hz}$ reduces $\beta$ from $5$ to $2.5$: the same <frequency deviation> acts for a shorter portion of each message cycle. A general message containing many <frequencies> does not have a single $f_m$ with this meaning.


 FM modulation index (source code)