When two waves with same frequency and constant phase difference interfere,

Options

A. there is a gain of energy
B. there is a loss of energy
C. the energy is redistributed and the distribution changes with time
D. the energy is redistributed and the distribution remains constant in time.

Answer

To solve the question regarding the interference of two waves with the same frequency and a constant phase difference, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Wave Interference**:
- When two waves interfere, they can either constructively or destructively interfere depending on their phase difference. Constructive interference occurs when the waves are in phase, while destructive interference occurs when they are out of phase.

2. **Same Frequency and Constant Phase Difference**:
- The problem states that the two waves have the same frequency and a constant phase difference. This means that the waves will consistently interfere in the same manner over time.

3. **Energy Conservation Principle**:
- According to the principle of conservation of energy, energy cannot be created or destroyed; it can only be transformed or redistributed. Therefore, the total energy of the system remains constant.

4. **Analyzing the Options**:
- We need to evaluate the options provided:
- Option 1: Gain of energy
- Option 2: Loss of energy
- Option 3: Energy is redistributed and the distribution changes with time
- Option 4: Energy is redistributed and the distribution remains constant in time

5. **Eliminating Incorrect Options**:
- Since energy cannot be gained or lost in this scenario, we can eliminate options 1 and 2.
- Now we need to determine whether the energy distribution changes with time or remains constant.

6. **Constant Phase Difference Implication**:
- With a constant phase difference, the interference pattern will remain stable over time. This means the redistribution of energy will not change; it will remain constant.

7. **Conclusion**:
- Therefore, the correct answer is option 4: "The energy is redistributed and the distribution remains constant in time."

### Final Answer:
The correct option is **4: The energy is redistributed and the distribution remains constant in time.**

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