Hello everyone!

I have viewed and read many papers on this subject but cant find any help to understand some point about how a short impulse duration situation affects rodīs motion.

To illustrate my point here is an example,

A small ball hits - a very fast impulse- one end of a long rod.
Now we know that the mechanical longitudinal - force carrying- propagation
wave through both objects take different times to propagate through each object due tue different lengths. This period, for the wave to propagate from the rodīs first end to the other end, and then to reflect back to the rodīs original end is much longer then the period of the small ballīs wave travel.

Lets assume that the ballīs impact/ impulse duration is shorter than the rodīs wave propagation period but is longer than the ballīs wave propagation period, i.e the ball hits the rod, has time to have its wave transmit/reflects and moves away, and right after is removed very quickly from the rod).

Now lets see if I understand this correctly:

First , in order for any object to move or- the rod in this case-, the wave from the original ball -impulse at the first end of the rod must propagate all the way to the other end of the rod and then back again to the first rod-end again. Only now when the wave has completed a full reflection that the motion force on the rod can reveal itself. Before that instant, no matter how hard the ball hits the rod, the rod itself can not move. (Of course, only local small compression and rarefaction of the rod + minor cg shifts occur during the wave propagation through the rod).

Here is my main question:
Now, keeping in mind that the impulse duration was shorter than the rodīs period , i.e. the ball "hit and run away" from the rod before the propagation wave inside the rod had time to reflect back. The ball is now no longer in contact with the rod. The wave in the rod is finally "after a long time" reflected back to the original rodīs first end on which the original impulse occurred, but there is no ball there touching!. Will the rod move even if the ball is no longer there touching that first rod-end ? Or will the rod only stay there since there is no ball for the rodīs reflected wave to push on? I know , I can already hear your thoughts now but that is why I am asking.

My point is actually not so complicated although it may very well sound so. If you are not understanding anything please dont hesitate to ask me to make anything clearer. I am surely making mistakes here so that is where your help comes in.
Oh by the way, the ball rod example is just a rather inefficient bad example,. the best method to have a very short impulse( hitting an object detaching near instantaneously) would be electromagnetic, i.e a capacitor bank discharge into a coil.

looking forward for your replies. Thanks.