# An 8-hour exposure to a sound intensity level of 90.0 dB may cause hearing damage. What energy in joules falls on a 0.800-cm-diameter eardrum so exposed?

Apr 23, 2015

You can use the relationship:
$I \left(\mathrm{dB}\right) = 10 \log \left(\frac{I}{I} _ 0\right)$
Where ${I}_{0} = {10}^{- 12} \frac{W}{m} ^ 2$ represents the intensity just audible (correspnding to $0 \mathrm{dB}$).
So:
$90 = 10 \log \left(\frac{I}{10} ^ \left(- 12\right)\right)$; power $10$ both sides and rearrange:
$I = 0.001 \frac{W}{m} ^ 2$
But Watts=(Joules)/(seconds)
and $8$ hours = $28800$ sec
and Area$= \pi {r}^{2} = 5 \times {10}^{-} 5 {m}^{2}$
Finally:
Energy$= 0.001 \cdot 28800 \cdot 5 \times {10}^{-} 5 = 0.00144 J$

Better check my maths!