A carrier signal C ( t ) = 25 (2 . 512 × 10 ^ 10 t) is amplitude modulated by a message signal m ( t ) = 5 (1 . 57 × 10 ^ 8 t) and transmitted through an antenna. What will be the bandwidth of the modulated signal ?

Correct answer: D. 50MHz Band width = 2 f _ m ω _ m = 1 . 57 × 10 ^ 8 = 2π f _ m BW = 2 f _ m = 10 ^ 8 2 Hz = 50MHz

JEE Main 202117 MarchEvening Shift

JEE Main 2021 · 17 March · Evening Shift · Physics · Communication System

A carrier signal C ( t ) = 25 (2 . 512 × 10 ^ 10 t) is amplitude...

A carrier signal

C ( t ) = 25\sin \left(2 . 512 \times {10}^{10}t\right)

is amplitude modulated by a message signal

m ( t ) = 5\sin \left(1 . 57 \times {10}^{8}t\right)

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

D. $50MHz$

Band width $= 2{f}_{m}$

${\omega}_{m} = 1 . 57 \times {10}^{8} = 2\pi{f}_{m}$

$BW = 2{f}_{m} = \dfrac{{10}^{8}}{2}Hz = 50MHz$