Slinky in Hand

Paul Doherty Oct '94

Making Transverse Waves

INTRODUCTION
Hold a slinky between your hands to model transverse wave resonances as well as longitudinal wave resonances which are like sound waves. Learn about nodes and antinodes of motion and pressure.

MATERIAL
A slinky
about 2 meters of 20 pound test monofilament fishing line
Optional substitute for nylon line, a smooth tabletop

ASSEMBLY
Tie the fishing line to a chair. After the first experiment slide the slinky onto the fishing line then tie the other end of the fishing line to another chair. Pull the chairs apart until the line is taut.
Optional, rest the slinky on a smooth table top. Use only 1/2 of a plastic slinky if you use a table top, otherwise friction will make the experiments difficult.

To Do and Notice

Hold the slinky between your hands. The slinky will be horizontal and sag. Move both of your hands up-and down together. Find the lowest frequency which produces the largest motion of the slinky for the smallest motion of your hands. (About one cycle per second.) One large hump, half-a-wave should appear moving up and down on the slinky.
Count the rhythm, 1,2,3,4,1,2,3,4,...

Move your hands in opposite directions, the right hand up when the left hand moves down and vice-versa. Move them in the same rhythm as above. Notice that your hands move a large distance. The center of the slinky does not move up-and-down at all.

What is Going On?

When you move your hands together you get a half-a-wave on the slinky the middle of the slinky is an antinode, the hand-held ends are nearly nodes.

When you move your hands opposite a half-a-wave also fits on the slinky. However this half wave has one node in the center and two antinodes near the hand-held ends.

The timing on both of these is the same. They both are one-half-wave resonances

ETC.
For the transverse motion of the slinky, pressure is modelled by the slope of the slinky. At places where the motion of the slinky passes through zero, a node of motion, the slope of the slinky changes the most, an antinode of slope.

Longitudinal Waves


To Do and Notice

The slinky should be on the monofilament line as described under assembly.

Grab the ends of the slinky in your hands.
Stretch the slinky to between 1 and 2 meters long.

Move your hands together and then apart, just as if you were clapping. Notice the motion of the slinky. Your hands move a lot while the center of the slinky moves very little. The center is a node.

Next notice the spacing between the slinks (turns) of the slinky. When the slinks are jammed close together the slinky models high pressures in a gas where the atoms are closer together. When the slinks are far apart the slinky models low pressure gas. Let’s call closely spaced slinks high pressure and widely spaced slinks low pressure. Notice that the pressure change is greatest at the center where the slinks alternately bunch-up and spread apart. Count the rhythm of this motion: 1,2,3,4,1,2,3,4,...

Move both hands in the same direction, if the slinky stretches right-left move both hands to the left then to the right. (One of our teachers described this as the buhdist clap, two one handed claps!)

Notice the motion of the slinky which is called longitudinal motion. Find the frequency of hand motion that produces the largest motion of the center of the slinky for the smallest motion of your hands. Count the rhythm of this motion: 1,2,3,4,1,2,3,4,...
Notice that the center of the slinky is an antinode, your hands are nearly nodes.
Notice that in the center the slinky moves back and forth but the spacing between the slinks near the center does not change. The center is an antinode of motion but a node ( a place with no change) of pressure.
At the nodes of motion near your hands however the slinks bunch together and then spread apart: the pressure changes a lot. The hand-held ends are antinodes of pressure.
Notice also that when one hand is at high pressure the other is low. The ends then swap the high pressure one becomes a low pressure and vice-versa. In other words, the slinks bunch up near one hand while they spread out at the other.

What is Going On?

When your hands move together one-half-wave of longitudinal motion fits on the slinky. This is the lowest frequency resonance of the slinky and it has what is called the fundamental frequency.

When your hands move opposite one-half-wave of longitudinal motion also fits on the slinky but this time the node is in the middle while your hands are near antinodes.

A sound wave is a longitudinal wave. A sound wave can be viewed either as a wave of motion of atoms or as a wave of pressure. In a standing sound wave nodes of motion occur at the same place as antinodes of pressure.

To Do and Notice

Find a higher frequency resonance of the longitudinal wave in which you move both hands in the same direction. You should have to move your hands about twice as often as in the lowest frequency resonance you created before.

Count the frequency: 1,2,3,4,1,2,3,4 Notice the motion of the slinky, there are two nodes each about 1/4 of the way from each end.
One full wave fits on the slinky.
When there is a high pressure near one node there is low pressure near the other. The high pressure and low pressure regions switch positions each cycle.

Move your hands opposite each other and find the next higher resonant frequency.

There will be three nodes on the slinky, one in the center and the other two1/6 of the slinky from each end.
3/2 of a wave fits on the slinky.
Notice the pressure changes on the slinky, when one node is experiencing high pressure the adjacent one experiences low pressure.
With time, each node oscillates from high pressure to low and back again.

What is Going On?

High pressure and low pressure nodes alternate in time as well as in space. To create an odd number of nodes move your hands opposite each other, clap hands. To create an even number of nodes move your hands in the same direction.

Etc

In the Exploratorium sound column a tall cement tube closed at both ends you can create a standing sound wave by playing an aluminum bar tuned to be in resonance with the column. When you place your ear at the floor, at a node of motion, the sound is loud, when you raise your ear to an antinode of motion the sound just about disappears.
This shows that your ear detects pressure changes. The floor is an antinode of pressure change.
The musical group “Lights in a Fat City” recorded the CD “Sound Column” in the Exploratorium sound column.