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

ManipalManipal 2012

Solution:

$L=10 \log _{10}\left(\frac{I}{I_{0}}\right)$
$\therefore L=10 \log _{10}\left(\frac{2 \times 10^{-8}}{10^{-12}}\right)$
$\left(\because I_{0}=10^{-12} W / m ^{2}\right)$
$L=10 \log _{10}\left(2 \times 10^{4}\right)$
$L=10\left[\log _{10} 2+\log _{10}(10)^{4}\right]$
$L=10(4.3)$
$L=43$ decibel