Doc-Al: Sorry, I did not know that.
However, it seems like the you overlook the fact that the rod is inelastic. The same thing goes for the answers in the thread you linked to.
And even if the rod was elastic, I do not buy your answer that the information/displacement will propagate as a wave pulse with the speed of sound in the medium. I am displacing the whole rod, so that the displacement is much higher that the wavelength of the pulse induced.