Assertion: A wire is stretched and then fixed at two ends. It oscillates in its second overtone mode. There are total four nodes and three antinodes.
Reason: In second overtone mode, length of wire should be `l=(3lambda)/2`, where `lambda` is wavelength.

Options

A. If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
C. If Assertion is true, but the Reason is false.
D. If Assertion is false but the Reason is true.

Explanation

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

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that a wire fixed at both ends oscillates in its second overtone mode, resulting in four nodes and three antinodes.
- In a standing wave pattern, nodes are points where the amplitude is zero, and antinodes are points where the amplitude is maximum.

2. **Identifying Nodes and Antinodes**:
- In the second overtone mode (which is the third harmonic), the pattern consists of:
- **Nodes**: 4 (including the ends)
- **Antinodes**: 3 (the points between the nodes)
- This matches the assertion, confirming that it is true.

3. **Understanding the Reason**:
- The reason states that in the second overtone mode, the length of the wire \( L \) is given by the formula \( L = \frac{3\lambda}{2} \), where \( \lambda \) is the wavelength.
- To verify this, we need to understand the relationship between the length of the wire and the wavelength in the context of standing waves.

4. **Calculating the Length of the Wire**:
- In the second overtone mode, the pattern consists of 3 antinodes and 4 nodes.
- The distance between two consecutive nodes is \( \frac{\lambda}{2} \) (half a wavelength).
- Therefore, the length of the wire can be calculated as:
- The distance from the first node to the last node (which includes 3 segments of \( \frac{\lambda}{2} \)):
- \( L = 3 \times \frac{\lambda}{2} = \frac{3\lambda}{2} \)
- This confirms that the reason is also true.

5. **Conclusion**:
- Both the assertion and the reason are true.
- However, the reason does not explain the assertion directly; it merely states a property of the second overtone mode.

### Final Answer:
- **Assertion**: True
- **Reason**: True
- **Conclusion**: Both statements are true, but the reason does not directly relate to the assertion.