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  4. The amplitude of 15 sin (1000 π t ) is modulated by 10 sin (4 π t ) signal. The amplitude modulated signal contains frequency (ies) of A. 500 Hz B. 2 Hz C. 250 Hz D. 498 Hz E. 502 Hz Choose the correct answer from the options given below:

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Q. 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. $500\,Hz$
B. $2\, Hz$
C. $250\, Hz$
D. $498\, Hz$
E. $502\, Hz$
Choose the correct answer from the options given below:

JEE MainJEE Main 2023Communication Systems

Solution:

Carrier wave frequency
$V _{ C }=\frac{100 \pi}{2 \pi}=500 \,Hz$
Modulating wave frequency
$ V _{ m }=\frac{4 \pi}{2 \pi}=2\, Hz$
$\therefore V _{ C }- V _{ m }, V _{ c }, V _{ c }+ V _{ m }$
$=498\, Hz , 500\, Hz , 502 \,Hz$