Answer
(a) $P_0 = 29~Pa$
(b) This pressure amplitude as a fraction of the atmospheric pressure is $2.9\times 10^{-4}$
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:
$P_0 = \sqrt{2I\rho v}$
$P_0 = \sqrt{(2)(1.0~W/m^2)(1.2~kg/m^3)(343~m/s)}$
$P_0 = 29~Pa$
(b) We can express this pressure amplitude as a fraction of the atmospheric pressure:
$\frac{29~Pa}{1.01\times 10^5~Pa} = 2.9\times 10^{-4}$
This pressure amplitude as a fraction of the atmospheric pressure is $2.9\times 10^{-4}$
