Question

A signal $A\cos \omega t$ is transmitted using $v_0\sin {\omega }_{0}t$ as carrier wave. The correct amplitude modulated $\left(AM\right)$ signal is

• A. $v_0\sin \left[{\omega }_0\right(1+0.1A\sin \omega t\left)t\right]$
• B. $v_0\sin {\omega }_{0}t+A\cos \omega t$
• C. $v_0\sin {\omega }_{0}t+$
  $\frac{A}{2}\left[\sin \right({\omega }_0-\omega )t+\sin ({\omega }_0+\omega \left)t\right]$
• D. $(v_0+A)\cos \omega t\sin {\omega }_{0}t$

Answer 1

The correct option is C $v_0\sin {\omega }_{0}t+$

$\frac{A}{2}\left[\sin \right({\omega }_0-\omega )t+\sin ({\omega }_0+\omega \left)t\right]$
Given signal $=A\cos \omega t$
The equation of amplitude modulated wave
$m=(v_0+A\cos \omega t)\sin {\omega }_{0}t$
$m=v_0\sin {\omega }_{0}t+A\cos \omega t\sin {\omega }_{0}t=v_0\sin {\omega }_{0}t+\frac{A}{2}\left[\sin \right({\omega }_0-\omega )t+\sin ({\omega }_0+\omega \left)t\right]$
$[\because 2\sin A\cos B=\sin (A+B)+\sin (A-B\left)\right]$

Hence option $\left(A\right)$ is correct.