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?

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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?

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Answer 1 · 2015-04-23T23:12:29

You can use the relationship:
$I (d B) = 10 log (\frac{I}{I_{0}})$ $I(dB)=10log(I/I_0)$
Where $I_{0} = 10^{- 12} \frac{W}{m^{2}}$ $I_0=10^(-12) W/m^2$ represents the intensity just audible (correspnding to $0 d B$ $0 dB$ ).
So:
$90 = 10 log (\frac{I}{10^{- 12}})$ $90=10log(I/10^(-12))$ ; power $10$ $10$ both sides and rearrange:
$I = 0.001 \frac{W}{m^{2}}$ $I=0.001 W/m^2$
But Watts=(Joules)/(seconds)
and $8$ $8$ hours = $28800$ $28800$ sec
and Area $= π r^{2} = 5 \times 10^{- 5} m^{2}$ $=pir^2=5xx10^-5m^2$
Finally:
Energy $= 0.001 \cdot 28800 \cdot 5 \times 10^{- 5} = 0.00144 J$ $=0.001*28800*5xx10^-5=0.00144J$

Better check my maths!

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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?

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