A massless string

  • Thread starter Thorazine
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Thorazine

So I have a wave incident on a boundary problem. The incidence is normal and the boundary is a knot of mass 'm' at z = 0, with the wave coming from minus infinity. The problem is that the string on the other side is massless, and I can't figure out exactly how that effects the boundary conditions. I know the string must be continuous as the first condition, and:

T*[df(+) - df(-)] = m*d^2f/dz^2

as the second condition. Where df(+) is the first derivative on the positive side of z = 0 and df(-) is the derivative on the negative side.

What I thought to do was let df(+) = 0 because there is no force coming from that side, but that hasn't worked. I also tried letting the transmitted wave be imaginary only because without mass I can't see how a string could vibrate, and that didn't work either. Any help would be much appreciated.
 
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Originally posted by Thorazine
What I thought to do was let df(+) = 0 because there is no force coming from that side...
Thorazine, I think this is physically correct. I think df/dz=0 everywhere in the massless part. Could you please explain why it doesn't work?
 
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I could be wrong but shouldn't the equation be:

m*[df(+) - df(-)]/dz = T*(d^2f/dz^2)


Maybe?
 

Thorazine

Re: Re: A massless string

Originally posted by arcnets
Thorazine, I think this is physically correct. I think df/dz=0 everywhere in the massless part. Could you please explain why it doesn't work?
I know it's not correct because it doesn't give me the right answer, I don't know why it doesn't work. :)
 

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