In a stationary wave, all particles of the medium cross the mean position with (

Options

A. different speeds at different instants
B. different speeds at the same instant
C. same speed at different instant
D. same speed at the same instant

Answer

To solve the question regarding the behavior of particles in a stationary wave as they cross the mean position, we can break it down into clear steps:

### Step 1: Understand the Concept of Stationary Waves
Stationary waves, also known as standing waves, are formed by the interference of two waves traveling in opposite directions. In a stationary wave, certain points (nodes) do not move, while others (antinodes) oscillate with maximum amplitude.

**Hint:** Remember that stationary waves are created by the superposition of two waves moving in opposite directions.

### Step 2: Analyze Particle Motion in Stationary Waves
In a stationary wave, all particles of the medium oscillate about a mean position. When the particles reach the mean position, they are at their equilibrium state, where the net force acting on them is zero.

**Hint:** Consider how particles oscillate around a central position and what happens when they reach that position.

### Step 3: Recognize the Timing of Particle Motion
At the mean position, all particles cross this point simultaneously. However, the speed of each particle varies depending on its position in the wave. Particles at the antinodes move faster than those at the nodes.

**Hint:** Think about how different positions in the wave affect the speed of the particles as they oscillate.

### Step 4: Conclude on Particle Speeds and Directions
While all particles cross the mean position at the same instant, they do so with different speeds and directions. This means that even though they reach the mean position simultaneously, their velocities differ due to their positions in the wave.

**Hint:** Focus on the relationship between position in the wave and the velocity of the particles.

### Final Answer
In a stationary wave, all particles of the medium cross the mean position with different speeds (or velocities) at the same instant.