A massless string

  • Thread starter Thorazine
  • Start date
  • #1
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.
 

Answers and Replies

  • #2
arcnets
508
0
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?
 
  • #3
Brad_Ad23
502
1
I could be wrong but shouldn't the equation be:

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


Maybe?
 
  • #4


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. :)
 

Suggested for: A massless string

Replies
19
Views
13K
  • Last Post
Replies
31
Views
2K
Replies
41
Views
13K
  • Last Post
Replies
22
Views
2K
  • Last Post
Replies
11
Views
1K
  • Last Post
Replies
7
Views
8K
Replies
5
Views
921
Replies
4
Views
833
  • Last Post
Replies
14
Views
1K
Replies
7
Views
1K
Top