A message signal of freuency `omega_(m)` is superposed on a carrier wave of frequency `omega_(c)` to get an amplititude modulated wave (AM). The frequency of the AM wave will be

Options

A. `omega_(m)`
B. `omega_(c)`
C. `(omega_(c)+omega_(m))/(2)`
D. `(omega_(c)-omega_(m))/(2)`

Explanation

To determine the frequency of the amplitude modulated (AM) wave when a message signal of frequency \( \omega_m \) is superposed on a carrier wave of frequency \( \omega_c \), we can follow these steps:

### Step 1: Understanding Amplitude Modulation
Amplitude modulation involves varying the amplitude of a carrier wave in accordance with the message signal. The carrier wave has a frequency \( \omega_c \), and the message signal has a frequency \( \omega_m \).

### Step 2: Formulating the AM Wave
The general form of an amplitude modulated wave can be expressed as:
\[ s(t) = [A_c + m(t)] \cdot \cos(\omega_c t) \]
where:
- \( A_c \) is the amplitude of the carrier wave,
- \( m(t) \) is the message signal which can be represented as \( A_m \cos(\omega_m t) \) (where \( A_m \) is the amplitude of the message signal).

### Step 3: Frequency Components of the AM Wave
When we modulate the carrier wave with the message signal, the resulting AM wave contains:
1. The original carrier frequency \( \omega_c \).
2. Sidebands at frequencies \( \omega_c + \omega_m \) and \( \omega_c - \omega_m \).

### Step 4: Conclusion on the Frequency of the AM Wave
Thus, the frequency components of the AM wave are:
- \( \omega_c - \omega_m \) (lower sideband)
- \( \omega_c \) (carrier frequency)
- \( \omega_c + \omega_m \) (upper sideband)

The overall frequency of the AM wave includes these components, but the carrier frequency \( \omega_c \) remains the dominant frequency.

### Final Answer
The frequency of the amplitude modulated wave consists of the carrier frequency \( \omega_c \) and the sidebands \( \omega_c + \omega_m \) and \( \omega_c - \omega_m \).

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