(A): All the particles between two consecutive nodes vibrate in the same phase.
(R): Particles on two sides of a node vibrate mutually in opposite phase

Options

A. Both 'A' and 'R' are true and 'R' is the correct, explanation of 'A'.
B. Both 'A' and 'R' are true and 'R' is not the correct explanation of 'A'
C. A' is true and 'R' is false
D. Both 'A' and 'R' are false

Answer

To solve the question, we need to analyze the assertion (A) and the reason (R) given in the problem.

**Assertion (A):** All the particles between two consecutive nodes vibrate in the same phase.

**Reason (R):** Particles on two sides of a node vibrate mutually in opposite phase.

### Step-by-Step Solution:

1. **Understanding Nodes and Antinodes:**
- In a standing wave, nodes are points where there is no displacement (particles are at rest), while antinodes are points of maximum displacement.

2. **Phase of Particles:**
- The phase of a particle in a wave refers to its position in the cycle of oscillation. Particles that are in the same phase oscillate together (i.e., they reach their maximum and minimum displacements at the same time).

3. **Particles Between Nodes:**
- Between two consecutive nodes, the particles oscillate with a certain amplitude. Since they are all part of the same wave segment, they will reach their maximum displacement, pass through equilibrium, and reach minimum displacement together. Hence, they vibrate in the same phase.

4. **Opposite Phase on Either Side of a Node:**
- On either side of a node, particles are moving in opposite directions. For example, if one particle is moving upwards (positive displacement), the particle on the other side of the node will be moving downwards (negative displacement). This means that they are 180 degrees out of phase, which is the definition of being in opposite phase.

5. **Conclusion:**
- Both the assertion (A) and the reason (R) are true statements. However, the reason (R) does not explain the assertion (A) directly. The assertion is about the particles between nodes, while the reason discusses the relationship of particles around a node.

### Final Answer:
- Both assertion (A) and reason (R) are true, but the reason is not the correct explanation for the assertion.