Let’s say I have a long pole, several miles long, and I push on it at one end.
Does the other end move instantaneously, or does it have to wait for the “wave” to travel to the other end before it moves?
A physics major told me years ago that the “wave” will travel at the speed of sound (in that material) and the other end will move with some delayed reaction.
So, for example, if you had pole that was a few dozen miles long, the other end might not move for several minutes.
Your friend was correct.
For the other end to move instantaneously, the material would have to be infinitely rigid. I have to look up what infinite rigidity does to the speed of sound in the medium but it makes it fast.
Woah there fella… be careful with that “thing”. 
As a general rule:
The speed of the motion
and the rythm of the rockin’
are equal to the notion
of the people interlockin’.
mipsman: Infinite rigidity, were it possible, would lead to infinite sound speed, but alas, this is yet another impossible ideal.
By the way, does anybody know where I can buy some of that massless, torsionless, unbreakable, unstretchable string that physics textbooks always talk about?
You get it in the same store that sells the perfect insulation mentioned in thermodynamics and fluid dynamics textbooks.
Silly.
Yeah, and don’t lean on the furniture in that store, since the tabletops are all frictionless planes.