A message signal of frequency 5 kHz is used to modulate a carrier signal of frequency 2 MHz.. The bandwidth for amplitude modulation is :

Options

A. 10 kHz
B. 2.5 kHz
C. 20 kHz
D. 5 kHz

Answer

To solve the problem of finding the bandwidth for amplitude modulation (AM) when a message signal of frequency \( f_m = 5 \, \text{kHz} \) is used to modulate a carrier signal of frequency \( f_c = 2 \, \text{MHz} \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Frequencies**:
- The frequency of the message signal, \( f_m = 5 \, \text{kHz} = 5 \times 10^3 \, \text{Hz} \).
- The frequency of the carrier signal, \( f_c = 2 \, \text{MHz} = 2 \times 10^6 \, \text{Hz} \).

2. **Understand the Bandwidth for AM**:
- The bandwidth \( B \) for amplitude modulation is given by the formula:
\[ B = 2f_m \]
- This formula indicates that the bandwidth is twice the frequency of the message signal.

3. **Calculate the Bandwidth**:
- Substituting the value of \( f_m \):
\[ B = 2 \times 5 \, \text{kHz} = 10 \, \text{kHz} \]

4. **Conclusion**:
- Therefore, the bandwidth for the amplitude modulation is \( 10 \, \text{kHz} \).

### Final Answer:
The bandwidth for amplitude modulation is \( 10 \, \text{kHz} \).

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