Answer
(a) $P_0 = 28.7~Pa$
(b) $F = 1.58\times 10^{-3}~N$
Work Step by Step
(a) We can find the intensity of the sound:
$\beta = 10~log\frac{I}{I_0}$
$120.0 = 10~log\frac{I}{I_0}$
$12.0 = log\frac{I}{I_0}$
$10^{12.0} = \frac{I}{I_0}$
$I = (10^{12.0})~I_0$
$I = (10^{12.0})~(1.0\times 10^{-12}~W/m^2)$
$I = 1.0~W/m^2$
We can use $343~m/s$ as the speed of sound in air.
We can use $\rho = 1.2~kg/m^3$ as the density of air.
We can find the pressure amplitude:
$P_0 = \sqrt{2I\rho v}$
$P_0 = \sqrt{(2)(1.0~W/m^2)(1.2~kg/m^3)(343~m/s)}$
$P_0 = 28.7~Pa$
(b) We can find the force exerted on the eardrum:
$F = P~A$
$F = (28.7~Pa)(0.550\times 10^{-4}~m^2)$
$F = 1.58\times 10^{-3}~N$
