Discussion
For \( \Delta f = 75 \ \mathrm{kHz} \) and \( f_m = 15 \ \mathrm{kHz} \), the modulation index is
Answer: D
Dividing deviation by message frequency:
\[ \beta = \frac{75}{15} = 5 \]
so 5, which is the deviation ratio of FM broadcasting at its highest audio frequency. 15 is the message frequency itself. 0.2 inverts the ratio and would describe narrowband FM. And 75 is the deviation quoted back. Because the index is largest for the lowest audio frequency, the worst-case bandwidth is computed at the highest audio frequency where the index is smallest, which is the point Carson's rule captures.
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