Consider an elastic ball is bounced off a hard flat surface. I would like to reconcile two different answers to the question "how does the contact time between the ball and surface depend on the speed of the ball?"
The first solution, which was the accepted solution here, is that the contact time is independent of the speed. It depends on the ball's diameter and the elasticity and density of its material. The signal for the ball to turn around is a compression wave that travels through the ball. The medium is non-dispersive.
The second solution, which seems to be more correct, is based on Hertzian contact mechanics. It claims that the bounce time is inversely proportional to the fifth root of the collision speed.
But what is the flaw in the first analysis? Is the speed of a compression wave through a sphere homogeneous material dispersive? Is the relevant distance that the wave travels equal to the amplitude of the indentation, not the diameter of the ball? This seems to be what the authors of the second solution are asserting, but I don't see how this is justified.