Standing Waves on a Hanging Chain
The speed of a wave along a chain depends on the tension and the mass density. A hanging chain of mass m supported at the top has a tension that varies from zero at the bottom to mg at the top. Nodes in standing waves in this chain are not evenly spaced because of this varying tension. In this experiment we oscillate the support of a chain of Christmas-tree beads and compare the resulting node spacing with the theoretical prediction.
This experiment was spotted by Dr. Ayars on a poster at the AAPT summer meeting in 2015. It has not yet been successfully done on this campus.
Reading
- A. B. Western, "Demonstration for observing J 0(x) on a resonant rotating vertical chain", American Journal of Physics 48:54 (1980)
- Richard A. Young, "Longitudinal standing waves on a vertically suspended slinky", American Journal of Physics 61:353 (1993)
Questions
- What is the wave speed as a function of distance from the end of the chain?
- Explain how an analysis using a single longitudinal wave is valid for this rotational system
- How are you going to measure the frequency?
Equipment needed
- Mardi-Gras bead string
- Something to measure node position (videocamera?)
- Stepper motor and stepper motor driver
- Mount for the stepper motor somewhere near the ceiling. (This will need to be built.)
- Function generator to drive stepper motor driver
- Some way of measuring drive frequency
Hazards
Mardi-Gras beads. Very dangerous.