Boundary Problem: Massless String with Knot of Mass 'm' at z=0

[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.

 

[arcnets]

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?

 

[Brad_Ad23]

I could be wrong but shouldn't the equation be:

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


Maybe?

 

[Thorazine]

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. :)