DIY · Card 57 · Physics · Waves
Two stools, a strip of duct tape, fifty skewers and a bag of jelly sweets. Tap one end and a wave you can actually watch ripples down the line, bounces off the far end and comes back.
01The brief
Slow a wave down until you can watch it.
50
skewers, each rocking on the spot as the wave goes by
2
ways a wave bounces: the same way up, or upside down
1959
the year John Shive’s wave machine starred in a famous film
Sound reaches your ears as a wave. So does light, and the Wi-Fi signal, and the swell on the sea. But most waves are far too fast, or too small, or invisible, to watch as they travel.
This machine slows one down to walking pace. A twist runs along a ladder of skewers, bounces off the end and comes back, and you can see every step. It shows nearly everything waves do: travelling, reflecting, passing through each other and standing still. It is a close cousin of the pendulum wave, though there the pendulums are not connected at all, and of Lenz’s law, another experiment where something invisible pushes back.
02Kit
Tape, skewers and sweets. Save a few sweets to eat.
Tick off what you have
0 of 6 ready
03Method
Even spacing and matching sweets are the secret to a smooth wave.
Step 1 of 8 · Minute 0
You need two stools or chairs of the same height, a roll of duct tape, about 50 wooden skewers, 100 jelly sweets such as gumdrops, two heavy books or rocks, scissors and a ruler.
The wave dies after a few skewers.
Why
The tape is slack, or the sweets are too heavy.
Fix
Pull the tape tighter between the stools, and use smaller sweets or move them closer to the tape.
The skewers flop over to one side.
Why
The sweets are unequal, or skewers aren’t centred.
Fix
Centre each skewer on the tape and use matching sweets at the same distance on both ends.
The wave is jerky.
Why
Uneven gaps between the skewers.
Fix
Use a ruler to space every skewer the same distance apart.
04Physics
Twist one skewer and the tape between it and its neighbour twists too, like a spring. That spring pulls the neighbour round, which twists the next bit of tape, and so on. Each skewer turns a moment after the one before, so the twist moves along the line, even though every skewer stays where it is.
Send a wave, change where the sweets sit, and see how the far end sends it back:
The wave runs at about 11 skewers a second. Slide the sweets out and each skewer gets harder to turn, so the wave slows down; slide them in and it speeds up. At a free end the last skewer swings out further and the wave comes back the same way up.
Keep sending waves at a steady rhythm and the ones going out meet the ones coming back. At certain rhythms they lock together into standing waves, with points that never move:
With both ends held, only certain rhythms fit: the line must hold a whole number of half-waves. 2 loops need a shake 2 times as fast as the slowest. The orange dots are nodes, where the wave going out and the wave coming back always cancel. A guitar string vibrates in exactly the same patterns.
05The big idea
Energy travels,
stuff stays.
A wave is a disturbance on the move. The skewers, the water, the air, they only rock back and forth. What crosses the room is energy, handed from each part to the next.
That is why the same few rules work for every wave there is. Sound, light, earthquakes and ripples all travel, reflect, pass through each other and form standing waves exactly as your sweets and skewers do.
06The math
1 · Wave speed
v = a √(κ ⁄ I)
Spacing a, tape twist-stiffness κ, skewer inertia I.
2 · Skewer inertia
I ≈ 2 m r²
Two sweets of mass m at distance r from the tape.
3 · Standing waves
fₙ = n v ⁄ 2L
Both ends held, line length L: n half-waves fit.
Because I grows with r² and the speed goes as 1 ⁄ √I, the wave speed is roughly proportional to 1 ⁄ r. Move every sweet from 10 cm to 5 cm from the tape and the wave should travel about twice as fast.
A wave that takes 4 s to cross a 2 m line is moving at 0.5 m/s. To make one loop of standing wave you would shake at f₁ = 0.5 ⁄ 4 ≈ 0.13 shakes a second, once every 8 s; two loops, every 4 s; three, every 2.7 s.
07Real life
From the ocean to the kitchen, the same rules at every scale.
Tsunamis
Ocean waves travel faster in deeper water. A tsunami crossing an ocean 4 km deep moves at around 700 km/h, as fast as a jet, then slows and rears up as the sea gets shallow near the shore.
Stadium waves
In a stadium wave, every fan just stands up and sits down, yet the wave races round the ground. It became world famous at the 1986 football World Cup in Mexico. Like your skewers, nobody moves along: only the disturbance does.
Earthquakes
Earthquakes send out several kinds of wave. The shear waves twist and shake the rock sideways as they pass, much like the twist running along your tape.
Guitar strings
Pluck a guitar string and waves run along it, bouncing off the two fixed ends. Only standing waves that fit a whole number of half-waves survive, and their rhythms are the notes you hear.
Echoes
Shout at a cliff and the sound wave bounces back, just as your twist bounces off the end of the tape. Bats and ships’ sonar time the echoes to find out how far away things are.
Microwave ovens
Microwaves bounce around inside the oven and make standing waves, with hot spots and cool nodes. That is why most ovens have a turntable: it moves the food through the hot spots so it cooks evenly.
1959
At Bell Telephone Laboratories, the physicist John Shive built a wave machine from steel rods welded across a thin twisting wire, the grown-up version of your skewers and tape. In 1959 he used it in a teaching film, Similarities in Wave Behavior, to show waves reflecting, passing through each other and standing still.
The film is still shown in physics classes today, and science museums around the world have Shive machines of their own. Your sweets and skewers work on exactly the same principle.
08Is and isn’t
A wave carries the stuff it travels through.
Each skewer only rocks back and forth on the spot. What travels is energy and the pattern of the disturbance, just as a stadium wave goes round while every fan stays in their seat.
A bigger push makes a faster wave.
A harder tap makes a bigger wave, not a faster one. The speed is set by the machine itself: the stiffness of the tape and how heavy the skewer ends are.
Waves just stop when they reach the end.
They reflect. A free end sends them back the same way up; a fixed end sends them back inverted.
Two waves meeting crash into each other.
They pass straight through each other. Where they overlap, their twists simply add up, then each carries on unchanged.
09Go further
A
Two waves at once
Tap both ends at the same moment. Watch the two waves meet in the middle. Do they bounce off each other or pass through?
B
Heavy and light
Make half the machine with sweets far out and half with them close in. What happens to a wave as it crosses the join? Does some of it bounce back?
C
Time it
Count the skewers and time how long a wave takes to cross. Work out its speed in skewers per second, then in metres per second.
D
Find the nodes
Hold both ends and wiggle one skewer near an end steadily. Slowly speed up until the line splits into loops. How many can you get?
E
Damp the end
Hang the last skewer’s sweets in a cup of water. Does the wave still bounce back as strongly?
10Questions
Stretch a strip of duct tape, sticky side up, between two stools about 2 metres apart. Press wooden skewers across it every 4 cm or so, push a jelly sweet onto both ends of each, and cover with a second strip of tape. Tap the first skewer and a wave runs down the line.
Each skewer is joined to its neighbours by the tape. Twist one and the tape twists, pulling the next skewer round a moment later, and so on down the line. The twist travels the whole length although each skewer only rocks in place. That travelling disturbance is a wave.
Weight far from the tape makes a skewer harder to start and stop turning; it has a larger moment of inertia. Each skewer then responds more sluggishly to the tug of the tape, so the wave travels more slowly. Bring the sweets in and it speeds up.
At the end there is nothing more to pass the twist to, so it is sent back. If the last skewer is free, it swings out extra far and the wave returns the same way up. If it is held, the tape is clamped and the wave returns upside down. Sound, light and water waves reflect in the same two ways.
The physicist John Shive at Bell Telephone Laboratories built a large version from steel rods on a twisting wire, and made it famous in the 1959 teaching film Similarities in Wave Behavior. The skewer-and-sweet version is a home-made copy of his idea.
Safety · Skewers have sharp points: push the sweets on carefully, and snip the points off for younger children. Don’t eat sweets that have been on the skewers.
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