The maximum intensities produced by two coherent waves of intensity `I_(1)` and `I_(2)` will be:

Options

A. `I_(1) + I_(2)`
B. `I_(1)^(2) + I_(2)^(2)`
C. `I_(1) + I_(2) + 2sqrt(I_(1)I_(2))`
D. zero

Answer

To find the maximum intensity produced by two coherent waves of intensity \( I_1 \) and \( I_2 \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Intensity Formula**:
The net intensity \( I_{\text{net}} \) at any point due to two coherent waves can be expressed as:
\[ I_{\text{net}} = I_1 + I_2 + 2\sqrt{I_1 I_2} \cos \phi \]
where \( \phi \) is the phase difference between the two waves.

2. **Maximizing the Intensity**:
To find the maximum intensity, we need to maximize the term \( \cos \phi \). The maximum value of \( \cos \phi \) is \( +1 \).

3. **Substituting the Maximum Value**:
Substitute \( \cos \phi = 1 \) into the intensity formula:
\[ I_{\text{max}} = I_1 + I_2 + 2\sqrt{I_1 I_2} \cdot 1 \]

4. **Simplifying the Expression**:
This simplifies to:
\[ I_{\text{max}} = I_1 + I_2 + 2\sqrt{I_1 I_2} \]

5. **Conclusion**:
Therefore, the maximum intensity produced by the two coherent waves is:
\[ I_{\text{max}} = I_1 + I_2 + 2\sqrt{I_1 I_2} \]

### Final Answer:
The maximum intensity produced by two coherent waves of intensity \( I_1 \) and \( I_2 \) is:
\[ I_{\text{max}} = I_1 + I_2 + 2\sqrt{I_1 I_2} \]