Standing waves can be produced

Options

A. on a string clamped at both the ends
B. on a string clamped at one end and free at the other
C. when incident wave gets reflected from a wall
D. When two identical waves with a phase difference of are moving in the same direction

Explanation

To solve the question regarding the conditions under which standing waves can be produced, we will analyze each option provided.

### Step-by-Step Solution:

1. **Understanding Standing Waves**:
- Standing waves are formed when two waves of the same frequency and amplitude travel in opposite directions and interfere with each other. This interference creates points of no displacement (nodes) and points of maximum displacement (antinodes).

2. **Analyzing Option A**:
- **Statement**: "On a string clamped at both ends."
- **Explanation**: When a string is clamped at both ends, waves traveling in opposite directions can reflect back and forth between the clamps. This results in the formation of standing waves with nodes at the clamps.
- **Conclusion**: This option is correct.

3. **Analyzing Option B**:
- **Statement**: "On a string clamped at one end and free at the other."
- **Explanation**: In this scenario, a wave traveling down the string will reflect off the fixed end (inverted reflection) and can interfere with the incoming wave. This setup can also produce standing waves, with a node at the clamped end and an antinode at the free end.
- **Conclusion**: This option is also correct.

4. **Analyzing Option C**:
- **Statement**: "When an incident wave gets reflected from a wall."
- **Explanation**: When a wave hits a wall, it reflects back. The incident wave and the reflected wave travel in opposite directions. The phase difference introduced by the reflection (180 degrees) allows for the formation of standing waves.
- **Conclusion**: This option is correct as well.

5. **Analyzing Option D**:
- **Statement**: "When two identical waves with a phase difference of r moving in the same direction."
- **Explanation**: For standing waves to form, the waves must travel in opposite directions. If they are moving in the same direction, they will not create the necessary interference pattern for standing waves.
- **Conclusion**: This option is incorrect.

### Final Answer:
The correct options for producing standing waves are **A, B, and C**.

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