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.

Answer

To solve the assertion and reason question, we need to analyze both statements provided in the question.

### Step 1: Understand the Assertion
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 defined as the difference between the upper and lower side frequencies.
- The upper side frequency (USB) is given by \( f_c + f_m \) and the lower side frequency (LSB) is given by \( f_c - f_m \).
- Therefore, the bandwidth \( B \) can be calculated as:
\[ B = (f_c + f_m) - (f_c - f_m) = 2f_m \]
This confirms that the assertion is true.

### Step 2: Understand the Reason
The reason states that "in case of amplitude modulation, the frequency of the modulated signal is equal to the frequency of the carrier wave."

- In amplitude modulation, the modulated signal consists of the carrier wave and the sidebands created by the modulating signal.
- The frequency of the modulated signal is not equal to the frequency of the carrier wave. Instead, it contains the carrier frequency \( f_c \) and frequencies \( f_c \pm f_m \) due to modulation.
- Therefore, this statement is misleading. The frequency of the modulated signal is not simply the frequency of the carrier wave; it includes additional frequencies due to modulation.

### Conclusion
- The assertion is true: the bandwidth of an AM signal is indeed \( 2f_m \).
- The reason is also true, but it does not correctly explain the assertion because it oversimplifies the relationship between the modulated signal and the carrier frequency.

### Final Answer
- The assertion (A) is true.
- The reason (R) is true but does not provide a correct explanation for the assertion.
- Therefore, the correct option is B: Assertion is true, Reason is true, but Reason is not the correct explanation for Assertion.

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