Answer
The power intercepted by an unprotected ear is $0.013~W$
Work Step by Step
(a) We can calculate the intensity of the sound wave as:
$\beta = 10~log(\frac{I}{I_0})$
$log(\frac{I}{I_0})= \frac{\beta}{10}$
$10^{log(\frac{I}{I_0})}= 10^{\frac{\beta}{10}}$
$I= I_0~10^{\frac{\beta}{10}}$
$I= (10^{-12}~W/m^2)~10^{\frac{130}{10}}$
$I = 10~W/m^2$
We then find the power received by the ear;
$P = I~A$
$P = I~(\pi~R^2)$
$P = (10~W/m^2)(\pi)(0.020~m)^2$
$P = 0.013~W$
The power intercepted by an unprotected ear is $0.013~W$.
