so before I tell you
tell me what you know about sound waves and what they can propagate through ?
Sound waves can propgate through solids, liquids and gases. I think one should say that sound waves are mechanical waves and not vice versa because mechanical waves are general and sound waves are specific.
They are one in the same a mechanical action for example .... striking a hammer on metal produces a sound wave
.... the mechanical action of the vibration of your vocal cords causes a sound wave
I don't think I could name a sound wave that isn't caused by a mechanical action
I believe the short answer to the OP question is: Hooke's Law.
No matter what the medium is, if you have a situation where distention increases the counter-force in a linear fashion, you will have a medium that allows wave propagation.
Mechanical waves are energy propagations across a structure through compression and stretching of the connected molecules making up the structure. The actual wave traveling is just the part of the structure that's currently reacting to the forces in order of next touching molecule and not the structure itself being moved