(A): In a longitudinal stationary wave a displacement node coincides with a pressure anti node.
(R): Restoring force is maximum at node and minimum at anti node.

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 given question, we need to analyze both the assertion (A) and the reason (R) provided.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states: "In a longitudinal stationary wave, a displacement node coincides with a pressure antinode."
- In longitudinal waves, particles oscillate back and forth in the direction of the wave. At a displacement node, there is no movement of particles, while at a pressure antinode, the pressure varies maximally.
- It is a known fact that in longitudinal waves, the displacement nodes (where particle displacement is zero) indeed coincide with pressure antinodes (where pressure variation is maximum).
- **Conclusion**: The assertion is **true**.

2. **Understanding the Reason (R)**:
- The reason states: "Restoring force is maximum at node and minimum at antinode."
- In longitudinal waves, the restoring force is related to the displacement of particles from their equilibrium position. At a node, where there is no displacement, the restoring force is actually **minimum** because the particles are not displaced.
- Conversely, at an antinode, where the displacement is maximum, the restoring force is **maximum** since the particles are at their farthest point from equilibrium.
- **Conclusion**: The reason is **false**.

3. **Evaluating the Relationship**:
- Since the assertion is true and the reason is false, we can conclude that the reason does not correctly explain the assertion.

4. **Selecting the Correct Option**:
- Based on our analysis, the correct option is: "Assertion is true and reason is false."

### Final Answer:
The correct option is: **Assertion is true and reason is false.**

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