During propagation of a plane progressive mechanical wave,

Options

A. All the particles are vibrating in the same phase.
B. Amplitude of all the particles is equal.
C. Particles of the medium executes SHM
D. Wave velocity depends upon the nature of the medium.

Explanation

To solve the question regarding the propagation of a plane progressive mechanical wave, we will analyze the properties of such waves step by step.

### Step 1: Understanding the Nature of the Wave
A plane progressive mechanical wave is characterized by the movement of particles in a medium. It is important to note that all particles in the medium oscillate around their equilibrium positions.

**Hint:** Consider how particles in a medium respond to a wave passing through them.

### Step 2: Phase of Particle Vibration
In a plane progressive wave, all particles of the medium vibrate in the same phase. This means that at any given moment, all particles reach their maximum displacement (amplitude) together.

**Hint:** Think about what it means for particles to be in the same phase during oscillation.

### Step 3: Amplitude of Particles
The amplitude of all particles in a plane progressive wave is the same. This uniformity in amplitude means that every particle experiences the same maximum displacement from its equilibrium position.

**Hint:** Recall the definition of amplitude in the context of wave motion.

### Step 4: Simple Harmonic Motion (SHM)
The particles of the medium execute Simple Harmonic Motion (SHM). This means that their motion can be described by sinusoidal functions, and they oscillate back and forth about their equilibrium positions.

**Hint:** Consider the characteristics of SHM and how they relate to wave motion.

### Step 5: Wave Velocity
The velocity of the wave depends on the nature of the medium through which it is traveling. Different materials will affect the speed of wave propagation due to their physical properties such as density and elasticity.

**Hint:** Reflect on how different materials can influence wave speed.

### Conclusion
Based on the analysis, we can summarize the properties of a plane progressive mechanical wave:
- All particles vibrate in the same phase.
- The amplitude of all particles is equal.
- Particles execute SHM.
- Wave velocity depends on the nature of the medium.

### Final Answer
The correct statements regarding the propagation of a plane progressive mechanical wave are:
- Amplitude of all particles is equal.
- Particles of the medium execute SHM.
- Wave velocity depends on the nature of the medium.