A 1000 kHz carrier is modulated with 800 Hz audio signals. What are the frequencies of first pair of side bands:

Options

A. 1000.8 kHz, 999.2 kHz
B. 999.2 kHz, 998.4 kHz
C. 1001.6 kHz, 1000.8 kHz
D. 1000 kHz, 800 Hz

Answer

To find the frequencies of the first pair of sidebands when a carrier wave is modulated by an audio signal, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- Carrier frequency (fc) = 1000 kHz
- Modulating frequency (fm) = 800 Hz = 0.8 kHz

2. **Understand the concept of sidebands:**
- When a carrier wave is modulated by an audio signal, it generates sidebands. The first pair of sidebands is created at frequencies:
- \( f_{c} + f_{m} \) (Upper Sideband)
- \( f_{c} - f_{m} \) (Lower Sideband)

3. **Calculate the upper sideband frequency:**
- Upper Sideband (USB) = \( f_{c} + f_{m} \)
- \( USB = 1000 \text{ kHz} + 0.8 \text{ kHz} = 1000.8 \text{ kHz} \)

4. **Calculate the lower sideband frequency:**
- Lower Sideband (LSB) = \( f_{c} - f_{m} \)
- \( LSB = 1000 \text{ kHz} - 0.8 \text{ kHz} = 999.2 \text{ kHz} \)

5. **State the final answer:**
- The frequencies of the first pair of sidebands are:
- Upper Sideband: 1000.8 kHz
- Lower Sideband: 999.2 kHz

### Final Answer:
- The frequencies of the first pair of sidebands are 1000.8 kHz and 999.2 kHz.