Which of the following statements is correct about the stationary waves

Options

A. All the particles of the medium vibrate in the same phase
B. Particles at the consecutive antinodes differ in phase by `pi`
C. Particles at the consecutive antinodes are in same phase
D. all the particles between consecutive nodes vibrate in phase

Answer

To determine which statements about stationary waves are correct, we will analyze each statement step by step.

### Step-by-Step Solution:

1. **Understanding Stationary Waves**:
- Stationary waves, also known as standing waves, are formed by the interference of two waves traveling in opposite directions. They do not propagate energy through the medium but instead create nodes and antinodes.

2. **Identifying Nodes and Antinodes**:
- In stationary waves, points of zero displacement are called **nodes**, and points of maximum displacement are called **antinodes**. At nodes, the particles of the medium do not move, while at antinodes, they oscillate with maximum amplitude.

3. **Analyzing the Statements**:
- **Statement 1**: "All the particles of the medium vibrate in the same phase."
- This statement is **incorrect**. In a stationary wave, particles at nodes are at rest (zero displacement), while particles at antinodes oscillate in opposite phases. Therefore, not all particles vibrate in the same phase.

- **Statement 2**: "Particles of the consecutive antinodes differ in phase by π."
- This statement is **correct**. Consecutive antinodes are always out of phase by π (180 degrees), meaning when one is at maximum positive displacement, the other is at maximum negative displacement.

- **Statement 3**: "Particles of the consecutive antinodes are in the same phase."
- This statement is **incorrect**. As established, consecutive antinodes are out of phase by π, not in the same phase.

- **Statement 4**: "All the particles between the consecutive nodes vibrate in phase."
- This statement is **correct**. Particles located between two consecutive nodes oscillate in the same phase, meaning they reach their maximum and minimum displacements simultaneously.

4. **Conclusion**:
- The correct statements about stationary waves are:
- Statement 2: "Particles of the consecutive antinodes differ in phase by π."
- Statement 4: "All the particles between the consecutive nodes vibrate in phase."

### Final Answer:
- The correct statements about stationary waves are:
- Statement 2 and Statement 4.