Semiconductors — JEE Main · 2021 · 25 Feb 2021 · Shift 1 Question with Solution

Given below are two statements :
Statement I:A speech signal of 2 kHz is used to modulate a carrier signal of 1 MHz . The bandwidth requirement for the signal is 4 kHz .
Statement II : The side band frequencies are 1002 kHz and 998 kHz .
In the light of the above statements, choose the correct answer from the options given below:

(A)Both Statement I and Statement II are true✓ Correct
(B)Statement I is true but Statement II is false
(C)Statement I is false but Statement II is true
(D)Both Statement I and Statement II are false

Answer: (A)

Solution

An amplitude modulated wave carries the carrier together with the two side bands at

f_{c} \pm f_{m}

, so the band of frequencies it occupies stretches from

f_{c} - f_{m}

f_{c} + f_{m}

and its width is

2 f_{m} = 2 \times 2 = 4

kHz. Statement I is true.

With

f_{c} = 1

MHz

= 1000

kHz and

f_{m} = 2

kHz, those side bands lie at

1000 + 2 = 1002

kHz and

1000 - 2 = 998

kHz. Statement II is true as well.

Both Statement I and Statement II are true.

JEE Main · 2021 · 25 Feb 2021 · Shift 1 · Single correct option

JEE Main · 2021 · 25 Feb 2021 · Shift 1 · Semiconductors

Solution

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