Question

Intensity level of sound whose intensity is${10}^{-8}W{m}^{-2}$ is ______ $dB$.

• A. $80dB$
• B. $8dB$
• C. $4dB$
• D. $40dB$

Answer 1

The correct option is D

$40dB$

Solution:

Step 1: Given information

Intensity$={10}^{-8}W{m}^{-2}$

Step 2: Calculate the intensity level of sound

Intensity, $I={10}^{-8}W{m}^{-2}$

Reference intensity, $I_0={10}^{-12}W{m}^{-2}$

$\Rightarrow L=10{\log }_{10}\left(\frac{{10}^{-8}}{{10}^{-12}}\right)$

$\Rightarrow L=10{\log }_{10}{10}^4$

$\Rightarrow L=40{\log }_{10}10$

$\Rightarrow L=40dB$

Hence, the correct option is (D).