The amplitude of \(15\sin (1000\pi t)\) is modulated by \(10\sin (4\pi t)\) signal. The amplitude modulated signal conta…
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The amplitude of \(15\sin (1000\pi t)\) is modulated by \(10\sin (4\pi t)\) signal. The amplitude modulated signal contains frequency(ies) of
A. \(500\mathrm{Hz}\)
B. \(2\mathrm{Hz}\)
C. \(250\mathrm{Hz}\)
D. \(498\mathrm{Hz}\)
E. \(502\mathrm{Hz}\)
Choose the correct answer from the options given below:
[JEE Main 2023, 31 Jan (Shift 1)]
✓ Correct answer: b)
A, D and E only
Explanation
Frequency of carrier wave
\({v}_{C}=\frac{1000\pi }{2\pi }=500\mathrm{Hz}\)
modulating wave
\({v}_{m}=\frac{4\pi }{2\pi }=2\mathrm{Hz}\)
Frequencies of the modelated wave
\(∴{v}_{C}-{v}_{m},{v}_{C},{v}_{C}+{v}_{m}\\ =498\mathrm{Hz},500\mathrm{Hz},502\mathrm{Hz}\)
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