A carrier signal $\mathrm{C}(\mathrm{t})=25 \sin \left(2.512 \times 10^{10} \mathrm{t}\right)$ is amplitude modulated by a message signal $\mathrm{m}(\mathrm{t})=5 \sin \left(1.57 \times 10^{8} \mathrm{t}\right)$ and transmitted through an antenna. What will be the bandwidth of the modulated signal?

JEE Main · 2021 · 17 Mar 2021 · Shift 2 · Semiconductors

A carrier signal

C (t) = 25 sin (2.512 \times 1 0^{10} t)

is amplitude modulated by a message signal

m (t) = 5 sin (1.57 \times 1 0^{8} t)

and transmitted through an antenna. What will be the bandwidth of the modulated signal?

Answer: (C)

For amplitude modulation, the bandwidth is twice the frequency of the message signal.

Message signal angular frequency:

ω_{m} = 1.57 \times 1 0^{8}

rad/s

Message signal frequency:

f_{m} = \frac{ω _{m}}{2 π} = \frac{1.57 \times 1 0 ^{8}}{2 π} = \frac{1.57 \times 1 0 ^{8}}{6.28} = 25 \times 1 0^{6}

Hz = 25 MHz

Bandwidth =

2 f_{m} = 2 \times 25

MHz = 50 MHz

JEE Main · 2021 · 17 Mar 2021 · Shift 2 · Single correct option