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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

JIPMERJIPMER 2011Electromagnetic Waves

Solution:

Let intensity of sound be $l$ and $l'$
Loudness of sound initially,
$\beta_{1}=10 \log \left(\frac{l}{l_{0}}\right)$
Later $\beta_{2}=10 \log \left(\frac{l'}{l_{0}}\right)$
Given, $\beta_{1}-\beta_{2}=20$
$\therefore 20=10 \log \left(\frac{l}{l^{\prime}}\right)$
or $l'=\frac{l}{100}$
Therefore, intensity decreases by a factor of $100 .$