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

[sophiecentaur]

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

 

[Jilang]

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.

 

[Saw]

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 (?).

 

[Jilang]

Ah, I've figured it out I think. The backward waves originating at different times must all cancel each other!

 

[sophiecentaur]

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).

 

[Jilang]

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...

 

[sophiecentaur]

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.