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  4. How many times more intense is a 90 dB sound than a 40 dB sound?

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Q. How many times more intense is a $90\, dB$ sound than a $40\, dB$ sound?

Uttarkhand PMTUttarkhand PMT 2010

Solution:

$90=10 \log _{10}\left(\frac{ I _{1}}{ I _{0}}\right) $
$\Rightarrow \frac{ I _{1}}{ I _{0}}=10^{9} \ldots$ (i)
Again, $ 40=10 \log _{10}\left(\frac{ I _{2}}{ I _{0}}\right) $
$\Rightarrow \frac{ I _{2}}{ I _{0}}=10^{4} \ldots$ (ii)
From Eqs.(i) and (ii), we get
$\frac{ I _{1}}{ I _{2}}=10^{5}$