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 (\(v\)), the 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 the order of (take multiplicative constant to be \(1)\)
1. \(10~\text{mm}\)
2. \(\dfrac{3}{100}~\text{mm}\)
3. \(1~\text{mm}\)
4. \(\dfrac{1}{10}~\text{mm}\)