Problems for
Intermediate Methods in Theoretical Physics

Edward F. Redish

Pulse to an Open End

An elastic string is attached to a teflon ring that is threaded over a steel rod that is rigidly fixed at both ends as shown in the figure below. The string is pulled taut and the ring can slide up and down the rod with negligible friction. You may also assume that we are looking at the figure from above and that the motion of the string and ring is horizontal so that gravity can be ignored.

(a) Suppose the ring has a very small mass. What can you say about the angle that the string pulling on the ring makes as the ring and string move up and down? (Hint: Consider drawing a free-body diagram for the ring.)

(b) A demonstrator (outside the figure on the right) holding the end of the string moves his hand up and down quickly creating a pulse of a shape f(x). Write a general solution of the wave equation on this string and interpret the terms.

(c) The figure at right is taken from the first edition of a popular standard textbook. In the first column is shown a pulse approaching and reflecting from a fixed end. In the second column is shown a pulse approaching and reflecting from a free end (ring sliding on a frictionless rod). At least six (6!) of the figures are incorrect. State which and explain why.

This page prepared by

Edward F. Redish
Department of Physics
University of Maryland
College Park, MD 20742
Phone: (301) 405-6120
Email: redish@umd.edu

Last revision 4. November, 2004.