(A): Velocity of particles, while crossing mean position (in stationary waves) varies from maximum at antinodes to zero at nodes.
(R): Amplitude of vibration at antinodes is maximum and at nodes, the amplitude is zero. And all particles between two successive nodes cross the mean position together.

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 both the assertion (A) and the reason (R) provided in the context of stationary waves. Let's break it down step by step.

### Step 1: Understanding Stationary Waves
Stationary waves are formed by the interference of two waves traveling in opposite directions. They consist of nodes (points of no displacement) and antinodes (points of maximum displacement).

**Hint:** Remember that stationary waves are characterized by fixed points (nodes) and points of maximum movement (antinodes).

### Step 2: Analyzing the Assertion (A)
The assertion states that the velocity of particles while crossing the mean position varies from maximum at antinodes to zero at nodes.

- At the mean position, particles have maximum velocity because they are moving through their equilibrium position.
- At nodes, the displacement is zero, and therefore, the velocity is also zero since the particles are not moving.

**Hint:** Think about how the motion of particles changes as they move from the antinode to the node.

### Step 3: Analyzing the Reason (R)
The reason states that the amplitude of vibration at antinodes is maximum, and at nodes, the amplitude is zero. It also mentions that all particles between two successive nodes cross the mean position together.

- The amplitude is indeed maximum at antinodes, where particles experience the greatest displacement.
- At nodes, the amplitude is zero, meaning there is no movement at those points.
- All particles between two nodes vibrate in phase, meaning they reach the mean position simultaneously.

**Hint:** Consider how the properties of waves (like amplitude and phase) affect the motion of particles in a stationary wave.

### Step 4: Conclusion
Both the assertion and the reason are true. The reason correctly explains the assertion as it describes the relationship between amplitude, velocity, and phase in stationary waves.

**Final Answer:** Both the assertion (A) and the reason (R) are true, and the reason is the correct explanation for the assertion.