A message signal of frequency \( \omega_{m} \) is superposed on a carrier wave of frequency \( \omega_{c} \) to get an amplitude modulated wave (AM). The frequency of the AM wave will be :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( \omega_c \)
In amplitude modulation the message changes only the amplitude of the carrier; the carrier keeps its own frequency.
\( \displaystyle c_m(t) = A_c\left(1 + \mu\sin\omega_m t\right)\sin\omega_c t \)
The wave oscillates at \( \omega_c \), and its envelope rises and falls at the message frequency \( \omega_m \). Expanding the product shows the carrier at \( \omega_c \) together with two side bands at \( \omega_c - \omega_m \) and \( \omega_c + \omega_m \), placed symmetrically about \( \omega_c \). So the frequency of the AM wave is the carrier frequency \( \omega_c \).
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 ωc – ωm and ωc + ωm are respectively called the lower side and upper side frequencies. The modulated signal now consists of the carrier wave of frequency ωc plus two sinusoidal waves each with a frequency slightly different from ωc, known as side bands.”