Waves and boundary conditions

1. Mar 6, 2006

mathlete

I'm given the fact that two strings under tension T are joined by a knot of mass m... i'm supposed to find the appropriate boundary conditions. I know that the tensions are the same in both ropes and that the boundary will be continuous. I know the "trick" in this problem is knowing the derivatives don't equal because of the knot of mass m, but I don't really know how to formulate it. Can anyone provide a nudge in the right direction?

2. Mar 6, 2006

Physics Monkey

You can make progress by making of use of Newton's laws for the massive knot while remembering that the string is continuous. In other words, the boundary conditions have to insure that the massive knot, which is a point but with non-infinitesimal mass, stays with the string.

3. Mar 7, 2006

mathlete

I understand that part, but I'm not sure how to formulate it... I get df/dz (from the left) - df/dz (from the right) = m/T but I don't think that's right.

4. Mar 7, 2006

Meir Achuz

Close.
1. Should =-mg/T.
2. You need sin\theta. (Unless you can make a small angle approx.)df/dz is tan\theta.

Last edited: Mar 7, 2006