Superposition of Pulses Behavior

[zorro]

Homework Statement

Two pulses with the same amplitude are moving toward each other on a rope as shown. Which of the following statements describes their behavior?

(A) They will reflect off of each other and reverse their directions.
(B) They will cancel out, leaving no pulses in the rope.
(C) They will combine to form a pulse of twice the amplitude.
(D) They will pass through each other.
(E) They will combine to form a standing wave.

The Attempt at a Solution

Here the pulses superimpose to cancel out their amplitudes. So the answer should be (B). But this is incorrect.

 

[ideasrule]

One of the somewhat counterintuitive results of wave mechanics is that waves seem not to affect each other at all--they pass right through each other. One way to see B is not correct is that energy must be conserved, and if the two waves completely cancel out, the rope would have no kinetic energy.

 

[zorro]

They are not waves, they are pulses. If they were waves then (E) would have been the answer.

 

[ckutlu]

I think this is just tricky. They will cancel out at "one point" leaving no pulses to be seen on the rope, however they will pass through each other, and continue to be pulses.

 

[zorro]

however they will pass through each other, and continue to be pulses.

By conservation of momentum?

 

[olivermsun]

The linear wave equation has traveling solutions of arbitrary form. You can have pulses or kinks or whatever else you want, and they will pass right through each other. As ckutlu points out, they will appear to "cancel" each other right at the moment where they overlap, but they will soon "reappear" as they pass by each other.