The intensity of a sound wave gets reduced by `20%` on passing through a slab. The reduction intensity on passage through two such consecutive slabs

Options

A. `40%`
B. `36%`
C. `30%`
D. `50%`

Explanation

To solve the problem of how the intensity of a sound wave is reduced when passing through two consecutive slabs, we can follow these steps:

### Step-by-Step Solution:

1. **Define Initial Intensity**:
Let the initial intensity of the sound wave be \( I_0 \).

2. **Calculate Intensity After First Slab**:
The intensity of the sound wave is reduced by 20% after passing through the first slab. Therefore, the intensity after the first slab, \( I_1 \), can be calculated as:
\[ I_1 = I_0 - 0.2 I_0 = 0.8 I_0 \]

3. **Calculate Intensity After Second Slab**:
The intensity after passing through the second slab is again reduced by 20%. Thus, the intensity after the second slab, \( I_2 \), can be calculated as:
\[ I_2 = I_1 - 0.2 I_1 = 0.8 I_1 \]
Substituting \( I_1 \):
\[ I_2 = 0.8 (0.8 I_0) = 0.64 I_0 \]

4. **Calculate the Reduction in Intensity**:
Now, we need to find the total reduction in intensity from the initial intensity \( I_0 \) to the final intensity \( I_2 \):
\[ \text{Reduction} = I_0 - I_2 = I_0 - 0.64 I_0 = 0.36 I_0 \]

5. **Calculate Percentage Reduction**:
To find the percentage reduction in intensity, we use the formula:
\[ \text{Percentage Reduction} = \left( \frac{\text{Reduction}}{I_0} \right) \times 100\% \]
Substituting the reduction we found:
\[ \text{Percentage Reduction} = \left( \frac{0.36 I_0}{I_0} \right) \times 100\% = 36\% \]

### Final Answer:
The intensity of the sound wave is reduced by **36%** after passing through two consecutive slabs.

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