# You hear a sound at 65 dB. What is the sound intensity level if the intensity of the sound is doubled?

You hear a sound at 65 dB. What is the sound intensity level if the intensity of the sound is doubled?
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Use the equation given by:
$\beta =\left(10dB\right){\mathrm{log}}_{10}\left(\frac{I}{{I}_{0}}\right)$
If l is doubled, use a property of logarithms to get the new value of the intensity level, ${\beta }^{\prime }$. We have:
${\beta }^{\prime }=\left(10dB\right){\mathrm{log}}_{10}\left(\frac{2I}{{I}_{0}}\right)\left(10dB\right)\left[{\mathrm{log}}_{10}\left(2\right)+{\mathrm{log}}_{10}\left(\frac{I}{{I}_{0}}\right)\right]$
$=\left(10dB\right){\mathrm{log}}_{10}2+\beta =3dB+65dB=68dB$
Result:
68dB