Sound waves of frequency $660 Hz$ fall normally on a perfectly reflecting wall. If the speed of sound is $330 m{s}^{-1},$ the shortest distance from the wall at which the air particles have the maximum amplitude of vibration is

Wavelength $\lambda =\frac{\mathrm{v}}{\mathrm{v}}=\frac{330}{660}=0.5\mathrm{m}=50\mathrm{cm}.$

The incident and reflected waves superpose to form standing waves in which the wall is a node. The particle amplitude is maximum at the antinode. The nearest antinode is at a distance $=\lambda /4=50 cm/4=12.5 cm$ from the wall.