Every so often someone asks more or less this question:
Could we communicate faster than light by taking a rigid rod longer than a light-year and simply pushing or pulling on one end?
Brett Evill replies:
Waves of compression and tension do not travel, even through solid materials, at infinite speed. Push on this end of a long rod and you squash it slightly. A wave of compression will propagate through the rod, eventually moving the far end away from you and restoring the original length of the rod (give or take resonance). This wave of compression will only travel at the speed of sound in the material that the rod is made out of.

I point out that since atoms in normal materials are held apart by electromagnetic forces, which travel (by definition) at the speed of light, the wave of compression cannot travel faster than light, because two neighbouring atoms cannot push on each other any faster than the force which connects them. If you can make a rod more rigid than this, why then, you have already gone beyond what relativity permits.