Question

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

• A. $1000$
• B. $10000$
• C. $10$
• D. $100$

Answer 1

The correct option is D $100$

Sound level is defined as

$\beta =10dBlo{g}_{10}\frac{I}{I_0}$

where $I_0$ is the threshold intensity of hearing $={10}^{-12}W{m}^{-2}$

Before attenuation, ${\beta }_1=10log\frac{I_1}{I_0}$
After attenuation, ${\beta }_2=10log\frac{I_2}{I_0}$

Given ${\beta }_2-{\beta }_1=-20$
$10log\frac{I_2}{I_0}-10log\frac{I_1}{I_0}=-20$
$log\frac{I_2}{I_0}-log\frac{I_1}{I_0}=-2$
$log\frac{I_2}{I_1}=-2$
$\Rightarrow I_2={10}^{-2}{I}_1=\frac{I_1}{100}$

So sound level decreases by $100dB$