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JEE Main 202228 JuneEvening Shift
Exam
JEE Main
Year
2022
Date
28 June
Shift
Evening Shift
Subject
Physics
Chapter
Communication System

JEE Main 2022 · 28 June · Evening Shift · Physics · Communication System

Amplitude modulated wave is represented by V _ AM = 10[1 + 0 . 4...

Amplitude modulated wave is represented by VAM=10[1+0.4cos⁡(2π×104t)]cos⁡(2π×107t){V}_{AM} = 10\left[1 + 0 . 4\cos \left(2\pi \times {10}^{4}t\right)\right]\cos \left(2\pi \times {10}^{7}t\right). The total bandwidth of the amplitude modulated wave is

Options

  1. A10kHz10kHz
  2. B20MHz20MHz
  3. C20kHz20kHz
  4. D10MHz10MHz

Correct answer

C. 20kHz20kHz

Step-by-step solution

Expression for modulation is given by,

s(t)=Ac[1+μcos(2πfmt)]cos⁡(2πfct)s\left(t\right) = {A}_{c}\left[1 + \mu cos\left(2\pi{f}_{m}t\right)\right]\cos \left(2\pi{f}_{c}t\right), where fm{f}_{m} and fc{f}_{c} are the frequency of the modulating signal and the carrier signal respectively.

Comparing it with the given expression in question, we get,

fm=104Hz{f}_{m} = {10}^{4}Hz

Now, Bandwidth =2fm=20kHz= 2{f}_{m} = 20kHz

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