Question

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?

Answer 1

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

Better check my maths!