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  4. A sound absorber attenuates the sound level by 20 dB. The intensity decreases by a factor of

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Q. A sound absorber attenuates the sound level by $20\, dB$. The intensity decreases by a factor of

NEETNEET 2022

Solution:

Let intensity of sound be $I$ and $I^{\prime}$.
Loudness of sound initially
$\beta_1=10 \log \left(\frac{I}{I_0}\right)$
Later, $\beta_2=10 \log \left(\frac{I^{\prime}}{I_0}\right)$
Given, $\beta_2-\beta_1=20$
$\therefore 20 =10 \log \left(\frac{I^{\prime}}{I}\right)$
$I^{\prime} =100 I$