Q 12-08-208JEE MainJEE Main 2019 (9 Apr, Shift 1)Easy
A signal $A\cos\omega t$ is transmitted using $v_0\sin\omega_0t$ as carrier wave. The correct amplitude modulated (AM) signal is
Answer: (D) $v_0\sin\omega_0t + \dfrac A2\sin(\omega_0 - \omega)t + \dfrac A2\sin(\omega_0 + \omega)t$
In AM the carrier amplitude varies with the signal:
$$c_m(t) = (v_0 + A\cos\omega t)\sin\omega_0t = v_0\sin\omega_0t + A\sin\omega_0t\cos\omega t$$
Using $2\sin X\cos Y = \sin(X - Y) + \sin(X + Y)$:
$$c_m(t) = v_0\sin\omega_0t + \frac A2\sin(\omega_0 - \omega)t + \frac A2\sin(\omega_0 + \omega)t$$
Solution by Sreeraj P, M.Sc Physics