Answer
The energy absorbed by the eardrum in 3.00 minutes is $1.08\times 10^{-6}~J$
Work Step by Step
We can find the intensity of the sound:
$\beta = 10~log\frac{I}{I_0}$
$80.0 = 10~log\frac{I}{I_0}$
$8.0 = log\frac{I}{I_0}$
$10^{8.0} = \frac{I}{I_0}$
$I = (10^{8.0})~I_0$
$I = (10^{8.0})~(1.0\times 10^{-12}~W/m^2)$
$I = 1.0\times 10^{-4}~W/m^2$
We can find the power on the eardrum:
$P = I~A$
$P = (1.0\times 10^{-4}~W/m^2)(0.600\times 10^{-4}~m^2)$
$P = 6.0\times 10^{-9}~W$
We can find the energy absorbed by the eardrum in 3.00 minutes:
$E = P~t = (6.0\times 10^{-9}~W)(180~s) = 1.08\times 10^{-6}~J$
The energy absorbed by the eardrum in 3.00 minutes is $1.08\times 10^{-6}~J$
