A signal

Question:

A signal Acos\omegat is transmitted using $v_{0} \sin \omega$ modulated (AM) signal is:

  1. (1) $v_{0} \sin \omega_{0} t+\frac{\mathrm{A}}{2} \sin$

    $\left(\omega_{0}-\omega\right) t+\frac{\mathrm{A}}{2}\left(\omega_{0}+\omega\right) t$

  2. (2) $v_{0} \sin \left[\omega_{0}(1+0.01\right.$ Asin\omegat $t]$

  3. (3) $v_{0} \sin \omega_{0} \mathrm{t}+\mathrm{A} \cos \omega \mathrm{t}$

  4. (4) $\left(v_{0}+\mathrm{A}\right) \cos \omega t \sin \omega_{0} t$


Correct Option: 1

Solution:

(1) The equation of amplitude modulated wave

$\mathrm{m}=\left(v_{0}+\mathrm{A} \cos \omega \mathrm{t}\right) \sin \omega \mathrm{t}$

$=v_{0} \sin \omega_{0} \mathrm{t}+\mathrm{A} \cos \omega \mathrm{t} \sin \omega_{0} \mathrm{t}$

$=v_{0} \sin \omega_{0} \mathrm{t}+\frac{\mathrm{A}}{2}\left[\sin \left(\omega_{0}-\omega\right) \mathrm{t}+\sin \left(\omega_{0}+\omega\right) \mathrm{t}\right]$

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