Answer
We can rank the sound waves in order of displacement amplitude, from largest to smallest:
$e \gt d = f \gt a \gt b \gt c$
Work Step by Step
We can write an expression for the displacement amplitude:
$s_0 = \frac{P_0}{\rho~v~\omega} = \frac{P_0}{2\pi~f~\rho~v}$
We can write an expression for the displacement amplitude in each case:
(a) $s_0 = \frac{0.05~Pa}{2\pi~(400~Hz)~\rho~v} = \left(\frac{1.25\times 10^{-4}}{2\pi~\rho~v}\right)~m$
(b) $s_0 = \frac{0.01~Pa}{2\pi~(400~Hz)~\rho~v} = \left(\frac{2.5\times 10^{-5}}{2\pi~\rho~v}\right)~m$
(c) $s_0 = \frac{0.01~Pa}{2\pi~(2000~Hz)~\rho~v} = \left(\frac{5.0\times 10^{-6}}{2\pi~\rho~v}\right)~m$
(d) $s_0 = \frac{0.05~Pa}{2\pi~(80~Hz)~\rho~v} = \left(\frac{6.25\times 10^{-4}}{2\pi~\rho~v}\right)~m$
(e) $s_0 = \frac{0.05~Pa}{2\pi~(16~Hz)~\rho~v} = \left(\frac{3.125\times 10^{-3}}{2\pi~\rho~v}\right)~m$
(f) $s_0 = \frac{0.25~Pa}{2\pi~(400~Hz)~\rho~v} = \left(\frac{6.25\times 10^{-4}}{2\pi~\rho~v}\right)~m$
We can rank the sound waves in order of displacement amplitude, from largest to smallest:
$e \gt d = f \gt a \gt b \gt c$
