You can see that a water wave does not carry the water with it. When ripples spread across a pond, a cork floating on the surface only moves up and down as each ripple passes. The cork stays in the same place, so the water under it is not travelling outwards with the ripples. It is the wave that travels.
Sound works in the same way. A loudspeaker makes the air particles next to it vibrate backwards and forwards. They push on their neighbours and the disturbance passes through the air. If the air itself travelled from the speaker to your ear, you would feel a strong wind every time someone spoke, and you do not.
Another piece of evidence is a bell ringing inside a sealed jar. As the air is pumped out, the sound gets quieter and quieter. Sound needs particles of a medium to pass the vibrations on, but it is the vibration that travels, not the air.
