The intensity of sound wave while passing through an elastic medium falls down by 10% as it covers one metre distance through the medium. If the initial intensity of the sound wave was 100 decibels, its value after it has passes through 3 metre thickness of the medium will be

Options

A. 70 decibel
B. 72.9 decibel
C. 81 decibel
D. 60 decibel

Explanation

To solve the problem step by step, we will analyze the decrease in intensity of the sound wave as it passes through the elastic medium.

### Step 1: Understand the initial intensity
The initial intensity of the sound wave is given as 100 decibels.

### Step 2: Determine the intensity reduction per meter
The intensity of the sound wave falls by 10% for every 1 meter it travels through the medium. This means that after 1 meter, the intensity will be:
\[ I' = I \times (1 - 0.10) = I \times 0.90 \]
Where \( I \) is the initial intensity.

### Step 3: Calculate the intensity after 1 meter
Using the initial intensity:
\[ I' = 100 \times 0.90 = 90 \text{ decibels} \]

### Step 4: Calculate the intensity after 2 meters
The intensity after the second meter will again fall by 10% of the intensity after the first meter:
\[ I'' = I' \times 0.90 = 90 \times 0.90 = 81 \text{ decibels} \]

### Step 5: Calculate the intensity after 3 meters
The intensity after the third meter will again fall by 10% of the intensity after the second meter:
\[ I''' = I'' \times 0.90 = 81 \times 0.90 = 72.9 \text{ decibels} \]

### Final Result
Thus, the intensity of the sound wave after it has passed through 3 meters of the medium is:
\[ I''' = 72.9 \text{ decibels} \]

### Conclusion
The answer is 72.9 decibels.

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