(A): In a harmonic progressive wave of a given frequency all particles have the same amplitude but different phases at a given instant of time.
(B) : In a stationary wave, all particles between two nodes have the same phase at a given instant but have different amplitudes.

Options

A. Both A and B are true
B. Both A and B are false
C. A is true, B is false
D. A is false, B is true

Answer

To analyze the statements (A) and (B) regarding harmonic progressive waves and stationary waves, we can break down the concepts step by step.

### Step 1: Understanding Harmonic Progressive Waves
A harmonic progressive wave is characterized by:
- **Same Amplitude**: All particles in the wave oscillate with the same maximum displacement from their equilibrium position.
- **Different Phases**: At any given instant, particles at different positions along the wave have different phases of oscillation. This means they reach their maximum and minimum displacements at different times.

### Step 2: Evaluating Statement (A)
Statement (A) claims:
- "In a harmonic progressive wave of a given frequency all particles have the same amplitude but different phases at a given instant of time."
- This statement is **True** because it accurately describes the nature of harmonic progressive waves.

### Step 3: Understanding Stationary Waves
A stationary wave (or standing wave) is characterized by:
- **Nodes and Antinodes**: Points where the wave has zero amplitude (nodes) and points where the amplitude is maximum (antinodes).
- **Same Phase Between Nodes**: All particles between two consecutive nodes oscillate in phase, meaning they reach their maximum and minimum displacements simultaneously.

### Step 4: Evaluating Statement (B)
Statement (B) claims:
- "In a stationary wave, all particles between two nodes have the same phase at a given instant but have different amplitudes."
- This statement is also **True** because particles between nodes oscillate in phase, but their amplitudes vary, being maximum at the antinodes and zero at the nodes.

### Conclusion
Both statements (A) and (B) are true based on the definitions and characteristics of harmonic progressive waves and stationary waves.

### Final Answer
- (A) is True.
- (B) is True.

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