A: The bandwidth of a modulated signal is `2f_(m)` in amplitude modulation, where `f_(m)` is the frequency of the modulating signal.
R: In case of amplitude modulation the frequency of a modulated signal is equal to the frequency of the carrier wave.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion
B. If both assertion and reason are true but reason is not the correct explanation of assertion
C. If assertion is true but reason is false
D. If both assertion and reason are false.

Answer

To analyze the statements provided in the question, we will break down the assertion (A) and the reason (R) step by step.

### Step 1: Understanding the Assertion (A)
The assertion states that "The bandwidth of a modulated signal is `2f_(m)` in amplitude modulation, where `f_(m)` is the frequency of the modulating signal."

- In amplitude modulation (AM), the bandwidth is indeed defined as the range of frequencies that the modulated signal occupies.
- The bandwidth of an AM signal is given by the formula:
\[ \text{Bandwidth} = 2f_m \]
where \( f_m \) is the frequency of the modulating signal.
- This is because the modulated signal will contain frequencies at \( f_c - f_m \) and \( f_c + f_m \), where \( f_c \) is the frequency of the carrier wave.

**Conclusion for Step 1**: The assertion is true.

### Step 2: Understanding the Reason (R)
The reason states that "In case of amplitude modulation, the frequency of a modulated signal is equal to the frequency of the carrier wave."

- In amplitude modulation, the carrier frequency \( f_c \) is the frequency at which the carrier wave oscillates.
- The modulated signal consists of the carrier frequency along with the sidebands created by the modulating signal.
- Therefore, while the carrier wave has a frequency \( f_c \), the modulated signal itself includes frequencies at \( f_c - f_m \) and \( f_c + f_m \), which means the frequency of the modulated signal is not equal to the frequency of the carrier wave.

**Conclusion for Step 2**: The reason is false.

### Final Conclusion
- Assertion (A) is true.
- Reason (R) is false.

Thus, the correct answer is that the assertion is true, but the reason is false.

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