Discussion
A signal m(f) = 5 sin (\(2\pi\) 100t) frequency modulates a carrier. The resulting FM signal is
{10 cos (\(2\pi\) \(10^{5}\)t) + 15 sin (\(2\pi\) 100 t)}.
The approximate bandwidth of FM signal is
Answer: C
The approximate bandwidth is 3.2 kHz. The message is \(5\sin(2\pi\,100\,t)\), so \(f_{m} = 100\) Hz, and the modulated signal carries a phase deviation of 15 rad, so the modulation index is \(\beta = 15\). Carson's rule gives
\[ BW \approx 2(\beta + 1) f_{m} = 2(15 + 1)(100) \]
\[ BW = 3200\ \text{Hz} = 3.2\ \text{kHz} \]
Options (A) and (B) are of the order of the message frequency alone and ignore the many significant sidebands that a modulation index of 15 produces. Option (D), 4 kHz, does not follow from Carson's rule for these values. The 100 kHz carrier frequency does not enter the bandwidth.
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