Regarding stationary waves, choose the correct options.

Options

A. (a) This is an example of interference
B. (b) Amplitudes of waves may be different
C. (c) particles at nodes are always at rest
D. (d) Energy is conserved

Answer

To solve the question regarding stationary waves and to choose the correct options, we will analyze each option step by step.

### Step-by-Step Solution:

1. **Understanding Stationary Waves**:
- Stationary waves are formed when two waves of the same frequency and amplitude travel in opposite directions and interfere with each other. This interference can be constructive or destructive, leading to the formation of nodes and antinodes.

**Hint**: Recall the definition of stationary waves and how they are formed through interference.

2. **Analyzing Option A**:
- **Statement**: "Stationary wave is an example of interference."
- **Evaluation**: This statement is correct. Stationary waves result from the interference of two waves traveling in opposite directions.

**Hint**: Consider how interference leads to the formation of stationary waves.

3. **Analyzing Option B**:
- **Statement**: "The amplitudes of the waves may be different."
- **Evaluation**: This statement is also correct. The two waves can have different amplitudes, and stationary waves can still form as long as they have the same frequency.

**Hint**: Think about the conditions required for stationary wave formation.

4. **Analyzing Option C**:
- **Statement**: "Particles at nodes are always at rest."
- **Evaluation**: This statement is incorrect. At the nodes, particles do not move up and down (they have zero displacement), but they are not at rest in terms of velocity. They are moving with maximum velocity at the mean position, not at the nodes.

**Hint**: Review the behavior of particles at nodes and antinodes in stationary waves.

5. **Analyzing Option D**:
- **Statement**: "Energy is conserved."
- **Evaluation**: This statement is correct. During the formation of stationary waves, energy is conserved. The energy can be transferred between kinetic and potential forms, but the total energy remains constant.

**Hint**: Consider the principle of conservation of energy in wave interactions.

### Final Evaluation of Options:
- **Option A**: Correct
- **Option B**: Correct
- **Option C**: Incorrect
- **Option D**: Correct

### Conclusion:
The correct options regarding stationary waves are A, B, and D.