In amplitude modulation, sinusoidal carrier frequency used is denoted by `omega_(c)` and the signal frequency is denoted by `omega_(m)`. The bandwidth `(Deltaomega_(m))` of the signal is such that `Deltaomega_(m)ltltomega_(c)`. Which of the following frequency is not contained in the modulated wave.

Options

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

Answer

To solve the problem, we need to analyze the frequencies present in an amplitude-modulated (AM) wave.

### Step-by-Step Solution:

1. **Understanding Amplitude Modulation**:
In amplitude modulation, a carrier wave of frequency \( \omega_c \) is modulated by a message signal of frequency \( \omega_m \). The modulated wave can be expressed as:
\[ V(t) = [A + m(t)] \cos(\omega_c t) \]
where \( A \) is the amplitude of the carrier and \( m(t) \) is the message signal.

2. **Frequency Components in AM**:
The modulated wave contains frequency components at:
- \( \omega_c + \omega_m \) (Upper side frequency)
- \( \omega_c - \omega_m \) (Lower side frequency)
- \( \omega_c \) (Carrier frequency)

3. **Identifying the Bandwidth**:
The bandwidth of the signal is given as \( \Delta \omega_m \) which is much less than \( \omega_c \) (i.e., \( \Delta \omega_m \ll \omega_c \)). This means that the frequencies \( \omega_m \) are significantly lower than the carrier frequency.

4. **Determining Frequencies Present in the Modulated Wave**:
From the above analysis, the frequencies present in the modulated wave are:
- \( \omega_c + \omega_m \)
- \( \omega_c - \omega_m \)
- \( \omega_c \)

5. **Identifying the Frequency Not Present**:
The frequency \( \omega_m \) itself is not present in the modulated wave. It is the frequency of the message signal, but it does not appear as a frequency component in the AM wave.

6. **Conclusion**:
Therefore, the frequency that is not contained in the modulated wave is \( \omega_m \).

### Final Answer:
The frequency that is not contained in the modulated wave is \( \omega_m \).