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Speed of sound

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• 1 hammer
• something hard and resonant (and inanimate) to bang it on
• 1 clock with a second hand
• 1 measuring tape
• 1 helper
• 1 pair of binoculars

Sound travels at 344 metres per second in air at 20 °C. This is slow enough for noises to be noticeably delayed when heard from even quite a short distance. You can use this effect to measure the speed of sound.

Ask your helper to a hit a wall or a piece of metal repeatedly with the hammer, about twice every second. The exact frequency of the beat doesn’t matter; it can be measured later. But the beat should be regular.

Now start walking away, looking back from time to time to watch your helper pounding away as you listen to the sound of their hammering. As the distance increases, the delay after each beat before the sound arrives will become longer and longer.

Eventually the delay will exactly match the time between each beat, and the sound will appear to arrive in time with the action of the hammer. At this point, dividing this distance by the time between beats gives you the speed of sound.

The time between each beat is easy to calculate from a count of the number of strikes during a short time period. The simplest way to measure the distance is to work out the average length of your step, and then count the number of paces between you and your helper. To measure the average length of your step, count the number of paces it takes you to cover a short distance measured out using the measuring tape.

Colour scattering

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• 1 glass of water
• 1 torch
• 1 small glass of milk

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The sky is blue because of a process called Rayleigh scattering. Light arriving from the Sun hits molecules in the air and scatters in all directions. The amount of scattering depends dramatically on the frequency of the light-its colour. Blue light, which has a high frequency, is scattered 10 times as strongly as red light, which has a lower frequency. So the scattered light that fills the sky is predominantly blue.

You can simulate this scattering in a glass of water by adding a few drops of milk and shining a torch through the mixture. Viewing the glass from the side, perpendicular to the beam of light, only scattered light is visible so the mixture looks blue.

This same process also explains why the Sun looks red at sunset. When the Sun is low on the horizon, its light has to pass a much longer distance through the atmosphere on its way to the Earth’s surface. On the way, blue light is scattered away, while red light, which is less susceptible to scattering, continues relatively unscathed.

Likewise, when you view the torch beam head-on through the milky mixture, you will find it has an orange tinge.

About turn

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• 1 roll of tape
• 16 or 20 large elastic bands

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You’d think that if you rotate an object through one full turn, it would end up as it was. But not according to quantum theory and the branch of mathematics known as group theory, which underlies it. For example, experiments with electrons show that they need to go through two full turns, rather than one, to get back to their initial state.

This weird property of our world can be demonstrated with a roll of tape and some elastic bands. Tie enough bands together to make four long strands, and attach them to the roll as shown. Now anchor the bands to some fixed objects. If you turn the roll around once, you will find that no amount of stretching the bands and looping them over one another will untangle it. The roll’s relationship to the world is tangled. But if you rotate the roll again in the same direction, so that it has now made two full turns, then there is a simple way, as shown here, to stretch the bands and untangle the roll.

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Cooking up DNA

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• ½ cup wheat germ
• salt
• lemon juice
• washing-up liquid
• alcohol (a neat spirit from the drinks cabinet will do)
• a tea strainer

You don’t have to squint down a microscope to catch sight of DNA. Although animal DNA is tiny, you can easily extract DNA from plant cells in your own kitchen, in less than an hour.

First, mix about half a wine glass full of wheat germ with about 150 millilitres of cold water, in which you have dissolved 1/3 of a teaspoon of salt and two squirts of lemon juice. This should be gently stirred for about 10 minutes to break down the plant’s cell walls. Press the mixture gently through the tea strainer and keep the pulp. Then repeat once more with the rest of the wheat germ.

Next, prepare 150 millilitres of cold water containing 1/3 of a teaspoon of salt, 3 teaspoons of alcohol and a couple of large drops of washing-up liquid. Add the pulp and stir. The detergent is now dissolving the DNA in the mixture. After 20 minutes of gentle stirring, add three heaped teaspoons of salt and stir the mixture for a further 10 minutes. Then leave it to stand until the solid settles out. Pour off the liquid and keep it. Throw the solid away.

Finally, dilute the liquid extract with about three times its volume of alcohol (clear spirits work best). As you stir, the plant DNA precipitates out as fine white threads which can be left to settle.

Miraculous unmixing

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• 2 cups salt
• 2 cups paprika or curry powder
• a window
• a large-format hardback book (such as an atlas), or a sheet of plywood
• a piece of paper rolled up to make a funnel

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Whether it’s dirty laundry, heaps of magazines and books, or a pocketful of coins, sorting a mixture into orderly piles is generally a chore. Not so for a mixture of salt and paprika.

To see why, first mix the salt and paprika in a jug or tall soft drinks bottle. Next, find a window with a frame against which you can press the book at the sides and the bottom, leaving a gap of a centimetre of so between the book and the glass. Use a ground-floor window so that you see the results from the other side.

Now roll the sheet of paper into a funnel, and use it to pour the salt-paprika mixture into the gap between the book and the window pane. Through the glass, you should see the mixture slide down the growing pile in a series of avalanches. In each avalanche, the salt and paprika will sort themselves out, depositing one layer of each on the surface of the pile, and leaving a streaked pile.