JEE Main 2016 · 10 Apr · Shift 1 · Physics Q24

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A modulated signal $C_m(t)$ has the form $C_m(t)=30\sin300\pi t+10(\cos200\pi t-\cos400\pi t)$ . The carrier frequency $f_c$ , the modulating frequency (message frequency) $f_\omega$ , and the modulation index μ are respectively given by :

f_c=200

Hz ;

f_\omega=50

Hz ;

\mu=\dfrac12

f_c=150

Hz ;

f_\omega=50

Hz ;

\mu=\dfrac23

f_c=150

Hz ;

f_\omega=30

Hz ;

\mu=\dfrac13

f_c=200

Hz ;

f_\omega=30

Hz ;

\mu=\dfrac12

Answer and worked solution

Official answer: B

$\cos200\pi t-\cos400\pi t=2\sin300\pi t\sin100\pi t$ , so
$C_m=30\sin300\pi t\left[1+\tfrac23\sin100\pi t\right].$
So $f_c=150$ Hz, $f_\omega=50$ Hz and $\mu=\frac23$ .

Topics:Modulation Trigonometric ratios and identities

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JEE Main 2016 · 10 Apr · Shift 1, Physics question 24