Which one of the following statements is incorrect for stable interference to occur between two waves?

Options

A. The waves must have the same wave length
B. The waves must have a constant phase difference
C. The waves must be transverse only
D. The waves must have equal amplitudes.

Explanation

To determine which statement is incorrect for stable interference to occur between two waves, we need to analyze the conditions required for stable interference.

### Step-by-Step Solution:

1. **Understanding Interference**:
- Interference occurs when two or more waves meet at a point and superpose to form a resultant wave. The resultant displacement is the vector sum of the individual displacements of the waves.

2. **Condition 1 - Same Wavelength**:
- For stable interference, the wavelengths of the two waves must be equal. This ensures that the waves can constructively and destructively interfere consistently over time.
- **Conclusion**: This statement is correct.

3. **Condition 2 - Constant Phase Difference**:
- The two waves must have a constant phase difference (denoted as φ). This means that the relative position of the waves does not change over time, allowing for stable interference patterns.
- **Conclusion**: This statement is also correct.

4. **Condition 3 - Type of Waves**:
- The statement that the waves must be transverse only is incorrect. Both transverse and longitudinal waves can exhibit interference. Thus, this condition is not necessary for stable interference.
- **Conclusion**: This statement is incorrect.

5. **Condition 4 - Equal Amplitude**:
- The waves do not need to have equal amplitudes for stable interference to occur. The resultant amplitude can be calculated using the formula:
\[ R = \sqrt{A_1^2 + A_2^2 + 2A_1A_2 \cos \phi} \]
- This shows that the amplitudes can be different and still produce stable interference.
- **Conclusion**: This statement is also incorrect.

### Final Answer:
The incorrect statements for stable interference to occur between two waves are:
- **Statement 3**: The waves must be transverse only.
- **Statement 4**: The waves must have equal amplitude.