## College Physics (4th Edition)

(a) $P_0 = 29~Pa$ (b) This pressure amplitude as a fraction of the atmospheric pressure is $2.9\times 10^{-4}$
(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 $2.9\times 10^{-4}$