The amplitude of $15 \sin (1000 \pi t)$ is modulated by $10 \sin (4 \pi t)$ signal. The amplitude modulated signal contains frequencies of 1. 500 Hz. 2. 2 Hz 3. 250 Hz 4. 498 Hz 5. 502 Hz Choose the correct answer from the options given below:

JEE Main · 2023 · 12 Apr 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 frequencies of

Choose the correct answer from the options given below:

Answer: (D)

A carrier of the form

15 sin (1000 π t)

has angular frequency

ω_{c} = 1000 π rad s^{- 1}

, so the carrier frequency is

f_{c} = \frac{1000 π}{2 π} = 500 Hz

. The modulating signal

10 sin (4 π t)

has

f_{m} = \frac{4 π}{2 π} = 2 Hz

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

f_{c}

f_{c} - f_{m}

and

f_{c} + f_{m}

. These evaluate to

500 Hz

500 - 2 = 498 Hz

and

500 + 2 = 502 Hz

. Hence the amplitude modulated signal contains the frequencies

498 Hz

500 Hz

and

502 Hz

JEE Main · 2023 · 12 Apr 2023 · Shift 1 · Single correct option