Finite length flexible strings with rigid end conditions when struck at somewhere other than the middle, say at 1/8th of the string's length, produce a pulse that propagates toward the boundary furthest away at a speed of c=sqrt(T/rho). When the pulse reaches the boundary there is an inversion and a reflection.
When struck in the middle the initial pulse widens with time. The widening wave reaches each boundary at the same time and reflects off the boundary but is not inverted. Why?
I think that the string will invert where the reflections from the ends meet again in the middle and then the whole string will invert spreading out from the centre. Before that, the reflections from the ends just cancel the original displacement so the string goes back to its original position.
I am not sure you are right about the difference. I think a similar thing happens when it is struck near the end, except that the reflection from the nearest end returns the string to the original position so it looks as if a pulse travels along the string towards the far end. At the far end, the reflection just cancels the displacement while the reflected and incident pulses overlap, then when the reflected pulse has passed the incident pulse it becomes an inverted pulse. The pulse will be twice as long as the separation between the point where the string was struck, and the end of the string, so for a string struck in the middle the pulse is as long as the string and is not apparent. If it is struck 1/8 from one end, the pulse will be 1/4 of the sting long but will only invert 1/8 from each end, because before that it overlaps its own tail.
My experience is in electronic delay lines, so I may be wrong, but I think the same principles apply.
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