End of Classical String - Boundary Condition Explained

[zwoodrow]

The free end of a classical vibrating string imposes the boundary condition that the spatial deriviative of the string at the end must be zero. I can hand wavingly argue this with free body diagrams and manipulate the differential force approximations but i can't come up with a terse intuitive explanation of this boundary equation. any help?

 

[bcrowell]

Another way of getting the result is that there is a 100% reflection of any disturbance propagating toward the end, and this reflection is uninverted. When you sum the incident and reflected waves, y(x) doubles, but y'(x) cancels.

This question belongs in the Classical Physics forum.

 

[atyy]

So that you get nice results?

Real strings have end corrections.

http://www.didjshop.com/physicsDidj02.html