In the transmission of sound through air, there is no actual movement of air from the sound producing body to our ear. The air layers only vibrate back and forth, and transfer the sound energy from one layer to the next layer till it reaches our ear. This back and forth motion causes the compression and rarefaction in a sound wave. This motion is along the direction of propagation of sound and hence, the sound waves are longitudinal. Note that the layers of air consist of molecules of gases. Note that the layers of air consist of molecules of gases. So, when the air layers vibrate back and forth, we actually mean that the molecules in air layers vibrate back and forth by a small distance.
Therefore, it simply means that air does not have modulus of rigidity.