A speech signal of `3 kHz` is used to modulate a carrier signal of frequency `1 MHz`, using amplitude modulation. The frequencies of the side bands will be

Options

A. 1.003 MHz and 0.997 MHz
B. 3001 kHz and 2997 kHz
C. 1003 kHz and 1000 kHz
D. 1 MHz and 0.997 MHz

Answer

To solve the problem of finding the frequencies of the sidebands in amplitude modulation, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Frequencies**:
- The frequency of the speech signal (modulating signal) is given as \( f_m = 3 \text{ kHz} \).
- The frequency of the carrier signal is given as \( f_c = 1 \text{ MHz} \).

2. **Convert Frequencies to the Same Unit**:
- Since \( f_m \) is in kilohertz and \( f_c \) is in megahertz, we need to convert \( f_m \) into megahertz for consistency.
- \( f_m = 3 \text{ kHz} = 0.003 \text{ MHz} \) (since \( 1 \text{ MHz} = 1000 \text{ kHz} \)).

3. **Calculate the Lower Sideband Frequency**:
- The frequency of the lower sideband (LSB) is calculated using the formula:
\[ f_{LSB} = f_c - f_m \]
- Substituting the values:
\[ f_{LSB} = 1 \text{ MHz} - 0.003 \text{ MHz} = 0.997 \text{ MHz} \]

4. **Calculate the Upper Sideband Frequency**:
- The frequency of the upper sideband (USB) is calculated using the formula:
\[ f_{USB} = f_c + f_m \]
- Substituting the values:
\[ f_{USB} = 1 \text{ MHz} + 0.003 \text{ MHz} = 1.003 \text{ MHz} \]

5. **Convert Sideband Frequencies to Kilohertz (if needed)**:
- If we want to express the sideband frequencies in kilohertz:
- \( f_{LSB} = 0.997 \text{ MHz} = 997 \text{ kHz} \)
- \( f_{USB} = 1.003 \text{ MHz} = 1003 \text{ kHz} \)

6. **Final Answer**:
- The frequencies of the sidebands are:
- Lower Sideband (LSB): \( 0.997 \text{ MHz} \) or \( 997 \text{ kHz} \)
- Upper Sideband (USB): \( 1.003 \text{ MHz} \) or \( 1003 \text{ kHz} \)

### Summary:
- Lower Sideband Frequency: \( 0.997 \text{ MHz} \) or \( 997 \text{ kHz} \)
- Upper Sideband Frequency: \( 1.003 \text{ MHz} \) or \( 1003 \text{ kHz} \)