I believe that if you push an object, say a metal pole, the disturbance travels through the object at the speed of sound in that material. In that case, what happens if you continuously push one end of the pole at the speed of sound? Does the pole keep getting compressed, since the disturbance would be traveling at the same speed as the end of the pole being pushed?
I'm adding an image to hopefully better explain the question.
In the image, we have a metal pole of length
L at time
t = 0. Let's say that the speed of sound through the pole is
v. Now, at
t = 0 we start pushing the pole at one end with speed
v. At time
t = L/2v, we've pushed one end of the pole by a distance
L/2. But, since the disturbance is also moving through the pole with speed
v, the disturbance has not reached the other end of the pole yet. So, that would mean that the other end of the pole has not moved yet. Does that mean that the pole now has a length