Yes it's true, but that doesn't last very long. It creates a compression of the molecules during exactly half of each vibe, and during the other half, it leans the other way, and the molecules spread out in what's called a "rarefaction" a region of lower-than-normal pressure. This 'train' of compressions and rarefactions is what travels through the air, away from the vibrating object, and it's what some people often call a "sound wave".
Yes, the playwright job is done once the play is officially finished.
