Shaken String Explorer

Explores the analytic form for waves on a string driven by harmonic motion of one support point.

A common introductory physics demonstration and lab entails observation of a taut stringwith one support point in driven harmonic transverse motion using an acoustic speaker or rotor. Resonant standing waves appears at modal requencies.

If the steady state wave amplitude is comparable to the amplitude of the motion of the driven end or if the drive frequency is close to zero and the string appears straight, the student may be unsure how to count the number of half-wavelengths. The locations of the nodes are also difficult to determine precisely even when a strobe light or fast video is used.

This script examines the analytic solution to the linearly damped wave equation with a harmonic boundary condition and demonstrates that the nodes are not stationary when damping is considered but are reflected in minima of an envelope function.

This script may interest students and instructors of physics and engineering. 'Try this' suggestions are included for further exploration.