Which of the following statements is correct?

Options

A. The distance between any two consecutive antinodes or nodes is `lamda/4`
B. The distance between a node and adjoining antinode is `lamda/4`
C. In the open end is an node.
D. In the closed end is an antinode.

Explanation

To solve the question, we need to analyze the statements provided about waves, nodes, and antinodes.

### Step-by-Step Solution:

1. **Understanding Nodes and Antinodes**:
- Nodes are points in a standing wave where there is no displacement (minimum amplitude).
- Antinodes are points where the displacement is maximum (maximum amplitude).

2. **Wavelength (λ)**:
- The distance between two consecutive nodes is equal to half the wavelength (λ/2).
- The distance between two consecutive antinodes is also equal to half the wavelength (λ/2).

3. **Distance Between Node and Adjoining Antinode**:
- The distance between a node and the nearest antinode is λ/4. This is because the wave oscillates from a node (zero displacement) to an antinode (maximum displacement) over a quarter of a wavelength.

4. **Open and Closed Ends**:
- In a closed-end tube, the closed end is a node (zero displacement), and the open end is an antinode (maximum displacement).

5. **Analyzing the Statements**:
- **Statement 1**: The distance between any two consecutive nodes is λ/2. (Correct)
- **Statement 2**: The distance between any two consecutive antinodes is λ/2. (Correct)
- **Statement 3**: The distance between a node and adjoining antinode is λ/4. (Correct)
- **Statement 4**: In an open end is a node, in the closed end is an antinode. (Incorrect)

6. **Conclusion**:
- Based on the analysis, the correct statement is that the distance between any two consecutive nodes is λ/2, and the distance between any two consecutive antinodes is also λ/2. The distance between a node and an adjoining antinode is λ/4. Therefore, the first statement is correct.

### Final Answer:
The correct statement is: The distance between any two consecutive nodes is λ/2.