Q 12-08-214JEE MainJEE Main 2019 (11 Jan, Shift 2)Medium
An amplitude modulated signal is plotted below. Which one of the following best describes the above signal?
Answer: (C) $\left(9 + \sin\left(2\pi\times10^4t\right)\right)\sin\left(2.5\pi\times10^5t\right)$ V
Envelope between $8$ V and $10$ V: carrier amplitude $A_c = 9$ V, modulation amplitude $A_m = 1$ V.
Modulating period $100\ \mu$s: $\omega_m = \dfrac{2\pi}{10^{-4}} = 2\pi\times10^4$ rad/s.
Carrier period $8\ \mu$s: $\omega_c = \dfrac{2\pi}{8\times10^{-6}} = 2.5\pi\times10^5$ rad/s.
$$V(t) = \left(9 + \sin\left(2\pi\times10^4t\right)\right)\sin\left(2.5\pi\times10^5t\right)\ \text{V}$$
Solution by Sreeraj P, M.Sc Physics