Assume that the displacement $(s)$ of air is proportional to the pressure difference $(\Delta p)$ created by a sound wave. Displacement $(s)$ further depends on the speed of sound $(v)$, density of air $(\rho)$ and the frequency $(f)$. If $\Delta p \sim 10\ \text{Pa}$, $v \sim 300\ \text{m/s}$, $\rho \sim 1\ \text{kg/m}^{3}$ and $f \sim 1000\ \text{Hz}$, then $s$ will be of the order of (take the multiplicative constant to be $1$)
Answer: (A) $\dfrac{3}{100}\ \text{mm}$
$s \propto \Delta p$, and the only combination of $v$, $\rho$, $f$ with dimensions of (length/pressure) is $\dfrac{1}{v\rho f}$:
$$[\Delta p] = ML^{-1}T^{-2},\quad [v\rho f] = LT^{-1}\cdot ML^{-3}\cdot T^{-1} = ML^{-2}T^{-2}$$
$$s = \frac{\Delta p}{v\rho f} = \frac{10}{300\times1\times1000} \approx 3.3\times10^{-5}\ \text{m} \approx \frac{3}{100}\ \text{mm}$$
Solution by Sreeraj P, M.Sc Physics