Discussion
For \( \Delta f = 75 \ \mathrm{kHz} \) and \( f_m = 15 \ \mathrm{kHz} \), Carson's rule gives
Answer: C
Applying the rule:
\[ B = 2(75 + 15) = 180 \ \mathrm{kHz} \]
so 180 kHz, which is why FM broadcast channels are spaced 200 kHz apart with a guard band. 150 kHz is twice the deviation, omitting the message term. 90 kHz is the sum without the factor of two. And 30 kHz is twice the message frequency, the AM figure. The comparison with AM's 30 kHz for the same audio shows exactly what FM spends to buy its noise performance.
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