If two sound waves of equal intensity I produce beats, then the maximum intensity of sound produced in beats will be

Options

A. I
B. 4 I
C. 2 I
D. `I//2`

Explanation

To find the maximum intensity of sound produced when two sound waves of equal intensity produce beats, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**:
We have two sound waves of equal intensity \( I \) (let's denote them as \( I_1 \) and \( I_2 \)). The problem states that these two waves produce beats.

2. **Identifying the Intensities**:
Since both waves have equal intensity, we can write:
\[ I_1 = I \quad \text{and} \quad I_2 = I \]

3. **Resultant Intensity Formula**:
When two waves interfere, the resultant intensity \( I_r \) can be expressed using the formula:
\[ I_r = I_1 + I_2 + 2\sqrt{I_1 I_2} \cos \phi \]
where \( \phi \) is the phase difference between the two waves.

4. **Substituting the Intensities**:
Substituting \( I_1 \) and \( I_2 \) into the formula:
\[ I_r = I + I + 2\sqrt{I \cdot I} \cos \phi \]
This simplifies to:
\[ I_r = 2I + 2I \cos \phi \]

5. **Maximizing the Resultant Intensity**:
To find the maximum intensity, we need to maximize the term \( \cos \phi \). The maximum value of \( \cos \phi \) is 1. Therefore, substituting \( \cos \phi = 1 \):
\[ I_r = 2I + 2I \cdot 1 = 2I + 2I = 4I \]

6. **Conclusion**:
The maximum intensity of sound produced in beats when two sound waves of equal intensity \( I \) interfere is:
\[ \boxed{4I} \]