as the sound save propagates from one place to the other in air, the air itself is not required to move from one place to the other

A vibrating object disturbs the air particles near it. The air particles get compressed as well as start vibrating and gain energy. These particles, vibrating about their mean position, then transfer their energy to the other layer of particles near to them. In this way region of compression and rarefaction are created and hence sound is produced. So, in sound production, only the transfer of energy of the vibrating particles takes place and not the transfer of particles themselves. So, yes we can say that as the sound wave propagates from one place to the other in air, the air itself is not required to move from one place to the other

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