Verified Solution • 2025–26 Session moderate

QJEEM23Ph64cb: JEE Main 2023 Physics - Class 12 JEEM23Ph64cb Solution: The amplitude of is modulated by signal. The amplitude…

The amplitude of 15sin⁡(1000πt)15 \sin (1000 \pi \mathrm{t}) is modulated by 10sin⁡(4πt)10 \sin (4 \pi \mathrm{t}) signal. The amplitude modulated signal contains frequency (ies) of

A. 500 Hz500 \mathrm{~Hz}

B. 2 Hz2 \mathrm{~Hz}

C. 250 Hz250 \mathrm{~Hz}

D. 498 Hz498 \mathrm{~Hz}

E. 502 Hz502 \mathrm{~Hz}

Choose the correct answer from the options given below:

Multiple Choice Options

  • A B only
  • B A only
  • C A, D and E only
  • D A and B only

Step-by-Step Verified Solution

Carrier wave frequency

VC=1000π2π=500 Hz\mathrm{V}_{\mathrm{C}}=\frac{1000 \pi}{2 \pi}=500 \mathrm{~Hz}

Modulating wave frequency

Vm=4π2π=2 Hz\mathrm{V}_{\mathrm{m}}=\frac{4 \pi}{2 \pi}=2 \mathrm{~Hz}

The amplitude modulated signal contains frequencies

=VC−Vm,VC,VC+Vm= \mathrm{V}_{\mathrm{C}}-\mathrm{V}_{\mathrm{m}}, \mathrm{V}_{\mathrm{C}}, \mathrm{V}_{\mathrm{C}}+\mathrm{V}_{\mathrm{m}}

=498 Hz,500 Hz,502 Hz=498 \mathrm{~Hz}, 500 \mathrm{~Hz}, 502 \mathrm{~Hz} .

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