Question

A sound has an intensity of $2\times 10^{-8}W/m^2$. Its intensity level in decibels is $\left({\log }_{10}2=0.3\right)$

• A. 23
• B. 3
• C. 43
• D. 4.3

Answer 1

Answer: (C)

$L=10{\log }_{10}\left(\frac{I}{I_0}\right)$
$\therefore L=10{\log }_{10}\left(\frac{2\times 10^{-8}}{10^{-12}}\right)$
$\left(\because I_0=10^{-12}W/m^2\right)$
$L=10{\log }_{10}\left(2\times 10^4\right)$
$L=10\left[{\log }_{10}2+{\log }_{10}(10{)}^4\right]$
$L=10(4.3)$
$L=43$ decibel