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 $100$

Loudness of sound, $L=10$ $lo{g}_{10}\frac{I}{I_o}$

$⟹$$L^{\prime }-L=10$ $lo{g}_{10}\frac{I^{\prime }}{I}$

The sound level attenuated by $20$ dB i.e $L^{\prime }-L=-20$ dB

$\therefore$ $-20=10$ $lo{g}_{10}\frac{I^{\prime }}{I}$

$\Rightarrow -2=lo{g}_{10}\frac{I^{\prime }}{I}$

$\Rightarrow$ $I^{\prime }={10}^{-2}I=\frac{I}{100}$

Thus, the intensity decreases by a factor of $100$.