JEE Main & Advanced Sample Paper JEE Main - Mock Test - 12

  • question_answer
    A modulated signal \[{{c}_{m}}(t)\] has the form\[{{c}_{m}}(t)=30sin300\pi t+10(cos200\pi t)-cos400\pi t)\]The carrier frequency \[{{\upsilon }_{c}},\]the modulating frequency (message frequency) \[{{\upsilon }_{m}},\], and the modulation index \[\mu \]are respectively given by

    A) \[{{\upsilon }_{c}}=200Hz;{{\upsilon }_{m}}=50Hz;\mu =1/2\]

    B) \[{{\upsilon }_{c}}=150Hz;{{\upsilon }_{m}}=50Hz;\mu =2/3\]

    C) \[{{\upsilon }_{c}}=150Hz;{{\upsilon }_{m}}=30Hz;\mu =1/3\]

    D) \[{{\upsilon }_{c}}=200Hz;{{\upsilon }_{m}}=30Hz;\mu =1/2\]

    Correct Answer: B

    Solution :

    [b]: Here, \[{{c}_{m}}(t)=30sin(300\pi t)+10(cos(200\pi t)-cos(400\pi t))\]Compare this equation with standard equation of amplitude modulated wave, \[{{c}_{m}}(t)={{A}_{c}}\sin {{\omega }_{c}}t-\frac{\mu {{A}_{c}}}{2}\cos ({{\omega }_{c}}+{{\omega }_{m}})t\] \[+\frac{\mu {{A}_{c}}}{2}\cos ({{\omega }_{c}}-{{\omega }_{m}})t\]


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