One of the components of frequency of amplitude modulated wave (AM) formed by the superposition of message signal of frequency `omega_1` on a carrier wave of frequency `omega_2 ` is

Options

A. `omega_1`
B. `omega_1/2`
C. `omega_2`
D. `(omega_1+omega_2)/2`

Answer

To solve the problem regarding the components of frequency in an amplitude-modulated (AM) wave formed by the superposition of a message signal of frequency \( \omega_1 \) on a carrier wave of frequency \( \omega_2 \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Components**:
- The message signal has a frequency \( \omega_1 \).
- The carrier wave has a frequency \( \omega_2 \).

2. **Formulate the AM Wave**:
- The general form of an amplitude-modulated wave can be expressed as:
\[ M(t) = A_c \sin(\omega_2 t) + \frac{A_m}{2} \cos((\omega_2 - \omega_1)t) + \frac{A_m}{2} \cos((\omega_2 + \omega_1)t) \]
- Here, \( A_c \) is the amplitude of the carrier wave, and \( A_m \) is the amplitude of the message signal.

3. **Identify Frequency Components**:
- From the equation, we can identify the frequency components:
- The carrier frequency \( \omega_2 \).
- The lower side frequency \( \omega_2 - \omega_1 \).
- The upper side frequency \( \omega_2 + \omega_1 \).

4. **Conclusion**:
- The frequency components of the amplitude-modulated wave are \( \omega_2 \), \( \omega_2 - \omega_1 \), and \( \omega_2 + \omega_1 \).
- Therefore, one of the components of frequency of the amplitude-modulated wave is \( \omega_2 \).

### Final Answer:
One of the components of frequency of the amplitude-modulated wave is \( \omega_2 \).

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