(A): In a progressive wave particle velocity and wave velocity are same.
(R): In a stationary wave energy is not confined to a limited region only.

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 analyze the given statements and determine their truthfulness, we will break down the concepts of progressive waves and stationary waves step by step.

### Step 1: Understanding Statement A
**Statement A**: "In a progressive wave, particle velocity and wave velocity are the same."

- In a progressive wave, the wave travels through a medium, and the particles of the medium oscillate around their equilibrium positions.
- The **wave velocity (v)** is the speed at which the wave propagates through the medium.
- The **particle velocity (v_p)** is the speed at which individual particles of the medium move as the wave passes.

In a progressive wave, these two velocities are not the same. The wave velocity is related to the distance traveled by the wave, while the particle velocity is related to the oscillation of the particles, which occurs perpendicular to the direction of wave propagation.

### Conclusion for Statement A:
- **Statement A is false.**

### Step 2: Understanding Statement R
**Statement R**: "In a stationary wave, energy is not confined to a limited region only."

- A stationary wave is formed by the interference of two progressive waves traveling in opposite directions.
- In a stationary wave, there are points called **nodes** where the amplitude is zero, and points called **antinodes** where the amplitude is maximum.
- The energy in a stationary wave is not uniformly distributed; it is concentrated at the antinodes and is minimal at the nodes.

Thus, the energy is confined to specific regions (the antinodes) and does not spread out uniformly.

### Conclusion for Statement R:
- **Statement R is false.**

### Final Conclusion:
Both statements A and R are false.

### Summary of the Solution:
1. **Statement A** is false because particle velocity and wave velocity in a progressive wave are not the same.
2. **Statement R** is false because in a stationary wave, energy is confined to specific regions (antinodes) and does not spread out.

### Final Answer:
Both A and R are false.

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