I have viewed and read several papers related to this subject but cant find any help to understand some seemingly a simple and a straitforward point, about whether a short impulse period compared to the wave propagation period in a rod may or may not fail to impart a motion on the rod. It seems that with a short duration impulse-contact between a ball and a long rod, no matter how powerful the impulse is , the struck/imparted long-rod would fail to accelerate/move due tue the rod´s wave propagation period being longer than the ball-rod contact impulse period(?)
To illustrate my point here is an example
A small ball hits one end of a long rod.(i.e a very short lived impulse on the rod where the ball "hits and runs away" from the rod.) let the two objects be made of the same material like steel, wood etc so that wave propagation speed is related only to length of rod or diameter of ball. Now we know that the mechanical longitudinal - force carrying- propagation wave starting right after the impact propagate through both the ball and rod it takes different times to propagate through each of them due Tue different lengths of the objects. This period, for the wave to propagate from the rod´s first end to the other rod´s end, and then to reflect back to the rod´s original first end is much longer then the period of the small ball´s wave travel.
Lets assume that the ball´s impact/ impulse duration is shorter than the rod´s wave propagation period but is longer than the ball´s wave propagation period, i.e the ball hits the rod, has time to have its wave transmitted/reflected and moves away, and right afterwards the ball is removed very quickly from the rod).
Now lets see if I understand this correctly:
First , in order for any object to move/accelerate 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 reflect 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 as a whole" can reveal itself and the rod as a whole can now accelerate forward away from its original place moving for miles and miles :). Before that instant, no matter how hard the ball hits the rod, the rod itself as a whole can not move/accelerate, i.e. can not displace itself away from its original location where it can reach the "end of the universe" - just exaggerating and clarify this very delicate simple point:). Of course, only local small compression and rarefaction of the rod + minor periodic cg shifts occur during the wave propagation through the rod and instantaneously with the impact..
Here is my main question:
Now, keeping in mind that the impulse duration was shorter than the rod´s wave 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 rod´s first end on which the original impulse occurred, but there is no ball there touching!. Will the rod now as a whole start to move/accelerate even if the ball is no longer touching the rod-end ? Or will the rod only stay there since there is no ball for the rod´s reflected wave to push on, and all motion we got is the compression wave going back and forth through the rod´s length? 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. It is truly appreciated Thanks. Regards