Why Are Both KE and PE Maximal at Equilibrium in a String Wave?

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Discussion Overview

The discussion revolves around the behavior of kinetic energy (KE) and potential energy (PE) in waves on a string, specifically questioning why both energies are maximal at the equilibrium position (y = 0) and minimal at maximum elongation (y = A or r). The scope includes theoretical interpretations and potential misconceptions regarding traveling and standing waves.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants express confusion about the claim that both KE and PE are maximal at the equilibrium position, suggesting that typically, one decreases as the other increases.
  • Others argue that PE should be minimal at the equilibrium position, contradicting the initial claim.
  • One participant provides a quote from Halliday's textbook, asserting that at y = 0, both KE and PE are indeed maximal, which raises further questions about the validity of this explanation.
  • A later reply discusses an article that claims Halliday's explanation is consistent with the behavior of traveling waves, where KE and PE are in phase, but questions its applicability to standing waves.
  • Another participant highlights the tension in the string and its relationship to potential energy, suggesting that the tension is assumed to be constant along the string.
  • Some participants differentiate between traveling and standing waves, debating whether the energy dynamics change based on the type of wave.
  • There is a discussion about the work done on a string element and how it relates to energy changes, with references to continuum mechanics and different methods of calculating work.
  • One participant proposes that the energy dynamics involve alternating between KE and PE, while another expresses uncertainty about the implications of the article referenced.

Areas of Agreement / Disagreement

Participants generally disagree on the relationship between KE and PE at the equilibrium position, with multiple competing views on the validity of Halliday's explanation and its implications for different types of waves. The discussion remains unresolved.

Contextual Notes

There are limitations regarding the assumptions made about wave types (traveling vs. standing) and the definitions of energy states in the context of string waves. Some participants express uncertainty about the implications of the tension in the string and how it relates to energy calculations.

  • #61
Yes but what is it that's actually 'moving along'? Nothing but the Energy. What's strange is that the energy goes one way and not the other - bearing in mind that the string (in a particular case) is just going up and down. Think that one over for a bit. lol
 
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  • #62
sophiecentaur said:
Yes but what is it that's actually 'moving along'? Nothing but the Energy. What's strange is that the energy goes one way and not the other - bearing in mind that the string (in a particular case) is just going up and down. Think that one over for a bit. lol

Yes, when you put it like that it certainly sound weird! Is there a natural propensity for energy to spread outwards? I'm imagining plucking a string and the wave traveling outwards in both directions. After that what keeps it going? Does the energy have an associated momentum outwards that must be conserved? I thought strings were pretty straightforward in 2013. Lol.
 
  • #63
It is a good point. I also think that the disturbance tends to move in both directions. When you pluck a string, it actually does. When a SHM device connected to a strig starts doing its job, again the disturbance attempts to move in both directions, but the fixed end where the device is prevents it from making progress in that direction (?).
 
  • #64
Ah, I've figured it out I think. The backward waves originating at different times must all cancel each other!
 
  • #65
Jilang said:
Ah, I've figured it out I think. The backward waves originating at different times must all cancel each other!
That sounds like good thinking. Do a Google search on Huygen's principle for predicting the progress of a wavefront of light. That's the more general case of what you just wrote and explains why the beam just carries on and only spreads out at the edges (i.e. it's a graphical way to explain diffraction).
 
  • #66
Thanks Sophie, That seems to be sort of thing indeed! It is a bit disconcerting though in as to how much Huygens Principle looks like it could be the earliest description of Quantum propagation. If this indeed the explanation of why the wave only goes one way it would appear that all classical waves are governed by quantum behaviour!

From what I can gather he assumed de facto that the waves only spread out forwards though. Later work seems to suggest that the backwards cancellation only works properly in an odd number of dimensions. So string yes, water no (!), space yes. Fascinating stuff...
 
  • #67
Jilang said:
Thanks Sophie, That seems to be sort of thing indeed! It is a bit disconcerting though in as to how much Huygens Principle looks like it could be the earliest description of Quantum propagation. If this indeed the explanation of why the wave only goes one way it would appear that all classical waves are governed by quantum behaviour!

From what I can gather he assumed de facto that the waves only spread out forwards though. Later work seems to suggest that the backwards cancellation only works properly in an odd number of dimensions. So string yes, water no (!), space yes. Fascinating stuff...

That makes it difficult to plot with a paper and pencil then! Just as well I never bothered to try in detail.
 

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