If two sources have a randomly varying phase difference f(t), the resultant intensity will be given by:

Options

A. `2I_(0)`
B. `I_(0)//2`
C. `2I_(0)`
D. `I_(0)//sqrt(2)`

Answer

To solve the problem, we need to understand the concept of intensity from two incoherent sources with a randomly varying phase difference.

### Step-by-Step Solution:

1. **Understanding Incoherent Sources**:
- Incoherent sources are those that do not have a fixed phase relationship. This means that the phase difference between the two sources can change randomly over time.

**Hint**: Remember that incoherent sources do not interfere constructively or destructively in a predictable manner.

2. **Intensity of Individual Sources**:
- Let the intensity of each source be \( I_0 \).

**Hint**: The intensity of a wave is proportional to the square of its amplitude, but here we are given the intensity directly.

3. **Resultant Intensity of Incoherent Sources**:
- For incoherent sources, the resultant intensity is simply the sum of the individual intensities. Therefore, if we have two sources with intensities \( I_1 \) and \( I_2 \), the resultant intensity \( I \) is given by:
\[ I = I_1 + I_2 \]

**Hint**: This is a key property of incoherent sources; they add up linearly.

4. **Calculating Resultant Intensity**:
- Since both sources have the same intensity \( I_0 \), we can substitute:
\[ I = I_0 + I_0 = 2I_0 \]

**Hint**: Make sure to substitute the values correctly.

5. **Conclusion**:
- The resultant intensity of the two incoherent sources with randomly varying phase difference is \( 2I_0 \).

**Hint**: Always check if the sources are coherent or incoherent before applying formulas related to intensity.

### Final Answer:
The resultant intensity will be \( 2I_0 \).