STATEMENT-1: In amplitude modulation, the frequency of amplitude variation is much smaller than the frequency of modulated wave
STATEMENT-2 : Frequency of the signal is much smaller than the frequency of the carrier wave

Options

A. Statement-1 is True. Statement-2 is True
Statement-2 is a correct explanation for statement-1
B. Statement is True Statement-2 is True
Statement-2 is NOT a correct explanation for Statement-1
C. Statement-1 Is True Statement-2 is False
D. Statement-1 is False. Statement 2 is True

Answer

To analyze the statements provided in the question, we can break down the concepts of amplitude modulation and the relationship between the modulating signal and the carrier wave.

### Step-by-Step Solution:

1. **Understanding Amplitude Modulation (AM)**:
- In amplitude modulation, a carrier wave is modulated by a lower frequency signal (the modulating signal). The carrier wave has a much higher frequency than the modulating signal.

2. **Defining the Frequencies**:
- Let the frequency of the modulating signal be represented as \( \omega_m \) (which is typically in the range of 20 Hz to 20 kHz).
- Let the frequency of the carrier wave be represented as \( \omega_c \) (which is usually in the range of a few MHz).

3. **Statement 1 Analysis**:
- Statement 1 claims that "In amplitude modulation, the frequency of amplitude variation is much smaller than the frequency of the modulated wave."
- The frequency of amplitude variation corresponds to the modulating signal frequency \( \omega_m \), while the frequency of the modulated wave is primarily determined by the carrier frequency \( \omega_c \).
- Since \( \omega_m \) is significantly smaller than \( \omega_c \), this statement is **true**.

4. **Statement 2 Analysis**:
- Statement 2 states that "The frequency of the signal is much smaller than the frequency of the carrier wave."
- This is a direct comparison between the modulating signal frequency \( \omega_m \) and the carrier frequency \( \omega_c \).
- Given that \( \omega_m \) is indeed much smaller than \( \omega_c \), this statement is also **true**.

5. **Correct Explanation**:
- Statement 2 correctly explains Statement 1 because it provides the rationale behind why the frequency of amplitude variation (the modulating signal) is much smaller than the frequency of the carrier wave.

6. **Conclusion**:
- Both statements are true, and Statement 2 is a correct explanation of Statement 1. Therefore, the answer to the question is that both statements are true, and Statement 2 is the correct explanation of Statement 1.

### Final Answer:
- **Both Statement 1 and Statement 2 are true, and Statement 2 is the correct explanation of Statement 1.**