Amplitude modulated signals contain frequencies: (\( \omega_c \) = carrier wave frequencies, \( \omega_m \) = modulating signal frequencies)
(A) \( \omega_c \)
(B) \( 2\omega_c \)
(C) \( \omega_c + \omega_m \)
(D) \( \omega_c - \omega_m \)
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A), (C) and (D) Only
In amplitude modulation the amplitude of the carrier \( A_c \sin\omega_c t \) is varied by the message \( A_m \sin\omega_m t \). With the modulation index \( \mu = A_m/A_c \):
\( \displaystyle c_m(t) = (A_c + A_m\sin\omega_m t)\sin\omega_c t \)
\( \displaystyle c_m(t) = A_c\sin\omega_c t + \frac{\mu A_c}{2}\cos(\omega_c - \omega_m)t - \frac{\mu A_c}{2}\cos(\omega_c + \omega_m)t \)
So the AM wave contains the carrier frequency and the two side bands \( \omega_c \pm \omega_m \).
(A) \( \omega_c \) — Correct. The first term is the carrier itself.
(B) \( 2\omega_c \) — Incorrect. No term at twice the carrier frequency appears in the expansion.
(C) \( \omega_c + \omega_m \) — Correct. It is the upper side band.
(D) \( \omega_c - \omega_m \) — Correct. It is the lower side band.
Note: This question is from the pre-rationalised NCERT book (2022-23). The topic was removed from the latest NCERT book (2026-27), and it also appears to be out of the CUET 2026 syllabus.
NCERT (Pre-rationalised edition, 2022-23):
Amplitude Modulation – “… Here \( \omega_c - \omega_m \) and \( \omega_c + \omega_m \) are respectively called the lower side and upper side frequencies. The modulated signal now consists of the carrier wave of frequency \( \omega_c \) plus two sinusoidal waves each with a frequency slightly different from \( \omega_c \), known as side bands.”