Two waves are said to be coherent, if they have

Options

A. same phase but different amplitude
B. same ferquency but different amplitude
C. same frequency, phase and amplitude
D. different frequnecy, phase and amplitude

Answer

To determine the conditions under which two waves are said to be coherent, we can analyze the definitions and properties of coherent waves step by step.

### Step-by-Step Solution:

1. **Understanding Coherence**:
Coherence refers to the correlation between two waves. For two waves to be coherent, they must maintain a constant phase relationship over time.

**Hint**: Think about what it means for two waves to be in sync with each other.

2. **Frequency Requirement**:
Coherent waves must have the same frequency. This ensures that the waves oscillate at the same rate, which is crucial for maintaining a constant phase difference.

**Hint**: Recall that frequency is the number of oscillations per unit time.

3. **Phase Relationship**:
Coherent waves must also have a constant phase difference. This means that the phase of one wave can be expressed as a fixed offset from the phase of the other wave.

**Hint**: Consider how the phase of a wave is represented mathematically and what it means for two waves to have a fixed phase difference.

4. **Amplitude Consideration**:
While the amplitude of coherent waves can be the same, it is not a requirement. Coherent waves can have different amplitudes and still be considered coherent as long as the frequency and phase conditions are met.

**Hint**: Think about how amplitude affects the height of the wave but not necessarily its timing or frequency.

5. **Evaluating the Options**:
Now, let’s evaluate the provided options:
- Option 1: Same phase but different amplitude (not sufficient).
- Option 2: Same frequency but different amplitude (not sufficient).
- Option 3: Same frequency, phase, and amplitude (sufficient).
- Option 4: Different frequency, phase, and amplitude (not coherent).

Based on the analysis, the only option that satisfies all the necessary conditions for coherence is Option 3.

6. **Conclusion**:
Therefore, two waves are said to be coherent if they have the same frequency, phase, and amplitude. However, it is important to note that while the amplitude can be the same, it is not a strict requirement for coherence.

**Final Answer**: Option 3 is correct: same frequency, phase, and amplitude.