Audio sine waves of 3 kHz frequency are used to amplitude modulate a carrier signal of 1.5 MHz. Which of the following statements are true?

Options

A. The side band frequencies are 1506 kHz and 1494 kHz
B. The bandwidth requried for amplitude modulation is 6kHz
C. The bandwidth required for amplitude modulation is 3 MHz
D. The side band frequencies are 1503 kHz and 1497 kHz

Explanation

To solve the question regarding the amplitude modulation of a carrier signal using audio sine waves, we will follow these steps:

### Step-by-step Solution:

1. **Identify the Given Frequencies**:
- The frequency of the audio sine wave (modulating signal) is given as \( f_m = 3 \, \text{kHz} \).
- The frequency of the carrier signal is given as \( f_c = 1.5 \, \text{MHz} \). Converting this to kHz gives \( f_c = 1500 \, \text{kHz} \).

2. **Calculate the Sideband Frequencies**:
- The sideband frequencies for amplitude modulation can be calculated using the formula:
\[ f_{SB} = f_c \pm f_m \]
- Substituting the values:
\[ f_{SB1} = 1500 \, \text{kHz} + 3 \, \text{kHz} = 1503 \, \text{kHz} \]
\[ f_{SB2} = 1500 \, \text{kHz} - 3 \, \text{kHz} = 1497 \, \text{kHz} \]
- Therefore, the sideband frequencies are \( 1503 \, \text{kHz} \) and \( 1497 \, \text{kHz} \).

3. **Determine the Bandwidth Required for Amplitude Modulation**:
- The bandwidth required for amplitude modulation is given by the formula:
\[ \text{Bandwidth} = 2 \times f_m \]
- Substituting the value of \( f_m \):
\[ \text{Bandwidth} = 2 \times 3 \, \text{kHz} = 6 \, \text{kHz} \]

4. **Evaluate the Options**:
- From the calculations:
- The sideband frequencies are \( 1503 \, \text{kHz} \) and \( 1497 \, \text{kHz} \) (which corresponds to Option 4).
- The bandwidth required is \( 6 \, \text{kHz} \) (which corresponds to Option 2).
- Therefore, the correct statements are:
- Option 2: The bandwidth required for amplitude modulation is \( 6 \, \text{kHz} \).
- Option 4: The sideband frequencies are \( 1503 \, \text{kHz} \) and \( 1497 \, \text{kHz} \).

### Final Answer:
The correct options are:
- Option 2: The bandwidth required for amplitude modulation is \( 6 \, \text{kHz} \).
- Option 4: The sideband frequencies are \( 1503 \, \text{kHz} \) and \( 1497 \, \text{kHz} \).