Question

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

• A. $23$
• B. $3$
• C. $43$
• D. $4.3$

Answer 1

The correct option is C $43$

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