Why does a wave pulse invert when it hits a fixed boundary on a string?

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Discussion Overview

The discussion revolves around the phenomenon of wave pulse inversion when it encounters a fixed boundary on a string. Participants explore the underlying principles and mechanics of this behavior, touching on concepts of wave dynamics and boundary interactions.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant inquires whether the inversion of the wave pulse is related to conservation of momentum.
  • Another participant asserts that conservation of momentum is not an issue, suggesting that a longitudinal wave would still exert a force on a fixed boundary, affecting the Earth’s orbit slightly.
  • One approach presented involves analyzing the scenario with a transverse wave, specifically considering the forces exerted by the wave on the boundary and the resulting force direction from the boundary back to the string.
  • Another point raised discusses the resultant displacement at the boundary due to both incident and reflected waves, questioning the direction of the reflected wave based on this displacement.

Areas of Agreement / Disagreement

Participants express differing viewpoints on the mechanics of wave inversion, with no consensus reached regarding the primary reasons behind the phenomenon.

Contextual Notes

Some assumptions about wave types (transverse vs. longitudinal) and their implications on force interactions are present but not fully explored. The discussion does not resolve the mathematical or conceptual details regarding the forces at play.

Jimmy87
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Hi, please could someone explain why a wave pulse traveling down a rope inverts when it strikes a fixed boundary. Is it something to do with conservation of momentum?
 
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There are no any problems with conservation of momentum: if we consider a longitudinal wave, then a wave pulse will push a fixed boundary which pushes the Earth which changes slightly its orbit.
 
At least two ways of understanding it...

(1) Assume (though we don't have to) that the wave is transverse and in the vertical plane, and that the pulse is an upward 'kink' in the rope. When the start of the kink reaches the wall it exerts an upward force on the wall. So what is the direction of the force that the wall exerts on the string (initiating the reflected wave)?

(2) What is the RESULTANT displacement of the string at the wall due to the incident and reflected waves? What therefore must be the direction of the reflected wave at the wall?
 

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