Making Waves
Hold a slinky between your hands, model transverse wave resonances as well as longitudinal wave resonances. Learn about nodes and antinodes of motion and compression.

• 2 chairs
• about 3 meters of 20 pound test monofilament fishing line
Optional substitute for nylon line, a smooth tabletop

No assembly needed.

 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 every time the middle of the slinky hits bottom, 1,2,3,4,1,2,3,4,... (If you have trouble, try this side to side on a table top).

Notice that the center of the slinky moves up and down the most and your hands the least. Move your hands in opposite directions, that is, move 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 whole the center of the slinky hardly moves at all. If you have trouble, try this on a table-top.

Count the rhythm every time your right hand hits bottom, 1,2,3,4,1,2,3,4,...

When you move your hands together you make a half-a-wave on the slinky the middle of the slinky is an antinode, a point of maximum motion while the hand-held ends are nearly nodes, points of no motion. 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, that is, the period is the same. They both are resonances in which one-half-wave fits onto the slinky. Both of these patterns of motion have the fundamental frequency of oscillation, the lowest frequency of motion for a slinky held at both ends. It is close to 1 hertz.

For the transverse motion 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. So at the same places where there are nodes of motion, there are antinodes of slope.

 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. If you use a table top, use only 1/2 of a plastic slinky, otherwise friction will make the experiments difficult.

When your hands move together one-half-wave of longitudinal motion fits on the slinky. This is the lowest frequency resonance of the slinky held at both ends, it 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 in a tube nodes of motion occur at the same place as antinodes of pressure. When both of your hands move together and apart as in a normal clap you are modelling sound waves in a tube closed at both ends. There are motion nodes at the ends and pressure antinodes. When you move both hands in the same direction, the non-clap, you are modelling a tube open at both ends. It has motion antinodes at the ends and pressure nodes.

Find a higher frequency resonance of the longitudinal wave in which you move both hands in the same direction (anti-clap). 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. Mark the nodes with flags of masking tape.

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 (clap) and find the next higher resonant frequency.

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nodes

There will be three nodes on the slinky, one in the center and the other two 1/6 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.

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.

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.

By
Paul Doherty

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