Discussion
A PM signal has an index of \( 0.3 \) radians. Its bandwidth for a \( 3 \ \mathrm{kHz} \) message is about
Answer: B
Applying the rule even at small index:
\[ B = 2 \times 3(1+0.3) = 7.8 \ \mathrm{kHz} \]
so 7.8 kHz, close to the narrowband limit of 6 kHz that the second option gives. That closeness is the point: below an index of about 0.3 the simple limit is adequate, and above it the full expression is needed. 1.8 kHz drops the factor of two and the unity term. And 12 kHz would need an index of one.
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