A signal of frequency 20 kHz and peak voltage of 5 volt is used to modulate a carrier wave of frequency 1.2 MHz and peak voltage 25 volts. Choose the correct statement.

Options

A. Modulation index = 5, side frequency bands are at 1400 kHz and 1000 kHz
B. Modulation index = 0.8, side frequency bands are at 1180 kHz and 1220 kHz
C. Modulation index = 0.2, side frequency bands are at 1200 kHz and 1180 kHz
D. Modulation index = 5, side frequency bands are at 21/2 kHz and 18.8 kHz

Answer

To solve the problem, we need to determine the modulation index and the sideband frequencies based on the given information about the modulating signal and the carrier wave.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Frequency of the modulating signal, \( f_m = 20 \text{ kHz} = 20 \times 10^3 \text{ Hz} \)
- Peak voltage of the modulating signal, \( V_m = 5 \text{ V} \)
- Frequency of the carrier wave, \( f_c = 1.2 \text{ MHz} = 1.2 \times 10^6 \text{ Hz} \)
- Peak voltage of the carrier wave, \( V_c = 25 \text{ V} \)

2. **Calculate the Modulation Index (\( \mu \)):**
The modulation index is given by the formula:
\[ \mu = \frac{V_m}{V_c} \]
Substituting the values:
\[ \mu = \frac{5 \text{ V}}{25 \text{ V}} = \frac{1}{5} = 0.2 \]

3. **Calculate the Sideband Frequencies:**
The sideband frequencies are calculated as follows:
- Upper sideband frequency (USB):
\[ f_{USB} = f_c + f_m = 1.2 \text{ MHz} + 20 \text{ kHz} = 1.2 \times 10^6 \text{ Hz} + 20 \times 10^3 \text{ Hz} = 1.220 \text{ MHz} = 1220 \text{ kHz} \]
- Lower sideband frequency (LSB):
\[ f_{LSB} = f_c - f_m = 1.2 \text{ MHz} - 20 \text{ kHz} = 1.2 \times 10^6 \text{ Hz} - 20 \times 10^3 \text{ Hz} = 1.180 \text{ MHz} = 1180 \text{ kHz} \]

4. **Summarize the Results:**
- The modulation index is \( 0.2 \).
- The upper sideband frequency is \( 1220 \text{ kHz} \).
- The lower sideband frequency is \( 1180 \text{ kHz} \).

### Final Answer:
The correct statement is that the modulation index is \( 0.2 \) and the sideband frequencies are \( 1220 \text{ kHz} \) and \( 1180 \text{ kHz} \).