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