Question

Do molecules of air undergo a displacement due to propagation of sound waves through them? comment

Answer 1

no they actually propagate on their mean position and remember the disturbance or the wave is moved forward not the molecules

Answer 2

Just put a cork on still surface of water nw produce waves at some distance from the cork...u will see waves moving forward but the cork moves only up and down at its own place....so every wave transports energy and not matter of the medium