The number of nodes and antinodes formed on a sonometer wire vibrating in second overtone are respectively.

Options

A. 2 node,2 3 antinodes
B. 3 nodes, 2 antinodes
C. 4 nodes, 2-antinodes
D. 3 nodes, 4 antinodes

Answer

To determine the number of nodes and antinodes formed on a sonometer wire vibrating in its second overtone, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Basics**:
- A sonometer wire is fixed at both ends, which means it can support standing waves.
- The fundamental frequency (first harmonic) has one antinode in the middle and nodes at both ends.

2. **Identifying Harmonics**:
- The first overtone is the second harmonic, which has two antinodes and three nodes.
- The second overtone is the third harmonic, which has three antinodes and four nodes.

3. **Counting Nodes and Antinodes**:
- For the second overtone (third harmonic), the pattern of nodes and antinodes can be visualized as follows:
- Nodes (N) are points where the string does not move.
- Antinodes (A) are points where the string moves with maximum amplitude.
- In the case of the second overtone:
- There are 4 nodes (including the fixed ends).
- There are 3 antinodes.

4. **Conclusion**:
- Therefore, the number of nodes and antinodes formed on a sonometer wire vibrating in its second overtone are 4 nodes and 3 antinodes respectively.

### Final Answer:
- The number of nodes is 4 and the number of antinodes is 3.

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