interferences of waves

Options

A. is the superposition of two waves with constant phase difference
B. is the maximum positive displacement in a transverse wave
C. in the maximum negative displacement in a transverse wave
D. is the superposition of two waves with variable phase difference

Answer

To solve the question regarding the interference of waves, we need to analyze the provided options based on the principles of wave interference.

### Step-by-Step Solution:

1. **Understanding Interference**:
Interference occurs when two or more waves overlap and combine to form a new wave pattern. For interference to happen, certain conditions must be met.

2. **Conditions for Interference**:
- **Two Waves**: Interference requires at least two waves.
- **Same Direction**: The waves must be traveling in the same direction.
- **Same Frequency**: The frequencies of the waves must be identical.
- **Constant Phase Difference**: The phase difference between the waves must be constant (either zero or a fixed value).

3. **Analyzing the Options**:
- **Option 1**: "Superposition of two waves with constant phase differences."
- This option satisfies the condition of having a constant phase difference. However, it does not explicitly mention the requirement for the same frequency and direction, but it is the best option among the given choices.
- **Option 2**: "Maximum positive displacement in a transverse wave."
- This describes amplitude, not interference. Therefore, this option is incorrect.
- **Option 3**: "Maximum negative displacement in a transverse wave."
- Similar to option 2, this describes amplitude in the negative direction, not interference. Thus, this option is also incorrect.
- **Option 4**: "Superposition of two waves with variable phase differences."
- This contradicts the requirement for constant phase difference necessary for interference. Therefore, this option is incorrect.

4. **Conclusion**:
Based on the analysis, the correct answer is **Option 1**: "Superposition of two waves with constant phase differences." This option aligns with the fundamental principles of wave interference.