JEE Main · 2023 · 31 Jan 2023 · Shift 1 · Semiconductors

The amplitude of

15 sin (1000 π t)

is modulated by

10 sin (4 π t)

signal. The amplitude modulated signal contains frequency(ies) of
(A) 500 Hz
(B) 2 Hz
(C) 250 Hz
(D) 498 Hz
(E) 502 Hz

Choose the correct answer from the options given below:

(A)A only
(B)A, D and E only✓ Correct
(C)B only
(D)A and B only

Answer: (B)

Solution

The carrier

15 sin (1000 π t)

has frequency

ν_{c} = \frac{1000 π}{2 π} = 500

Hz and the modulating signal

10 sin (4 π t)

has frequency

ν_{m} = \frac{4 π}{2 π} = 2

Hz. Amplitude modulation produces the carrier together with two sidebands at

ν_{c} \pm ν_{m}

, that is

500 - 2 = 498

Hz and

500 + 2 = 502

Hz. The frequencies present are therefore

498

Hz,

500

Hz and

502

Hz.

JEE Main · 2023 · 31 Jan 2023 · Shift 1 · Single correct option

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