Question
Answers

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
(A) $ {\omega _m} $
(B) $ {\omega _C} $
(C) $ \dfrac{{{\omega _C} + {\omega _m}}}{2} $
(D) $ \dfrac{{{\omega _C} - {\omega _m}}}{2} $

Answer
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Hint : It is a simple question. It will be easy to answer if we know the concepts correctly. We need to know what a carrier wave is, and we should know about the process of modulation of waves and types of modulations.

Complete step by step answer
Modulation is the process of changing amplitude or frequency or phase of the carrier wave in accordance with the intensity of the signal.
Some of the modulation process are,
-Amplitude modulation
-Frequency modulation
-Phase modulation
Amplitude modulation: When the amplitude of a high frequency carrier wave is changed in accordance with the intensity of the signal it is called amplitude modulation.
Frequency modulation: When the frequency of a carrier wave is changed in accordance with the intensity of the signal it is called frequency modulation.
Phase modulation: when the phase of the carrier wave is varied in accordance with the amplitude of the modulating signal and the rate of variation is proportional to the signal frequency is called phase modulation.
Carrier wave: A carrier wave is a high frequency electromagnetic wave that can be modulated in amplitude or in a frequency or in a phase modulation to carry signals.
Amplitude modulated wave: When a given carrier wave is superimposed with another high frequency wave in accordance with the intensity of the given carrier wave signal we get an amplitude modulated wave.
From the above discussion we can see that the frequency of the amplitude modulated wave and the frequency of the carrier wave will be the same.
Hence the correct answer is option (B) $ {\omega _C} $ .

Note
In amplitude modulation, the frequency of the carrier wave remains unchanged, so the frequency of the modulated wave is equal to the frequency of the carrier wave; it is the key concept to solve this question.