The gap between the frequency of the side bands in an amplitude modulated wave is

Options

A. twice that of the carrier signal
B. twice that of the message signal
C. the same as that of the message signal
D. the same as that of the carrier signal

Explanation

To solve the question regarding the gap between the frequency of the sidebands in an amplitude modulated wave, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Amplitude Modulation (AM)**:
- In amplitude modulation, a low-frequency message signal is superimposed on a high-frequency carrier wave. This process allows the transmission of the message signal over long distances.

2. **Identifying the Frequencies**:
- The carrier frequency is denoted as \( f_c \).
- The message signal frequency is denoted as \( f_m \).
- When amplitude modulation occurs, two sidebands are created:
- Lower Sideband (LSB): \( f_c - f_m \)
- Upper Sideband (USB): \( f_c + f_m \)

3. **Calculating the Gap Between Sidebands**:
- The gap between the frequencies of the sidebands can be calculated as:
\[ \text{Gap} = \text{USB} - \text{LSB} = (f_c + f_m) - (f_c - f_m) \]
- Simplifying this expression:
\[ \text{Gap} = f_c + f_m - f_c + f_m = 2f_m \]

4. **Conclusion**:
- The gap between the frequency of the sidebands in an amplitude modulated wave is \( 2f_m \), which is twice that of the message signal frequency.

### Final Answer:
The gap between the frequency of the sidebands in an amplitude modulated wave is **twice that of the message signal**.

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