1. To start with, you need to make a homemade drum. Cut the bottom of your plastic container to create a cylindrical shape with two open ends. Try and cut the bottom off as straight as possible so that the cylinder sits level on a table. If you have a suitably sized drum already, you can skip to step 7.
2. Cut out a circular piece of your plastic sheeting to be a few centimeters or inches larger in diameter than the top of your cylinder.
3. Using a piece of tape, stick one edge of your piece of plastic sheeting to the side of your cylinder.
4. Stretch the plastic sheeting tightly over the top of your cylinder and stick the opposite edge to the side of the cylinder.
5. Work your way around the cylinder, stretching and sticking the piece of plastic sheeting. You need to stretch the plastic sheeting as tightly and evenly as possible without tearing it.
6. To keep things from getting too messy later, make a collar for the top of your drum. Cut out a few strips of your piece of cardboard about 5 cm (2 in) wide and stick these end-to-end. Wrap this around the top of your ‘drum’ and fasten the ends with some tape.
7. Now we can start experimenting. What do you think will happen if you tap the top of your drum with your finger? Try it. What happens? Is this what you expected? What do you think makes the sound that you hear?
8. Now lift your drum up, holding your finger lightly on the plastic sheeting. What do you think you will feel if you shout into the bottom of the drum? Do this. What do you feel? What do you think is causing these vibrations? What happens if you shout louder or softer? What happens if you shout at a higher or lower pitch?
9. Place your drum on a table and sprinkle some sand, salt, or couscous onto the top. What do you think will happen if you sing a single note near the top of the drum? Do this and see if what you observe matches your predictions. What happens if you sing louder or softer? What happens if you sing lower or higher notes?
10. Connect your speaker to your mobile phone and open the tone generator app. A tone generator produces a ‘pure’ sound or tone of a single defined pitch and volume. Set the frequency to 200 Hz. Set the amplitude quite low. Play the sound. What do you think it will sound like if you increase the frequency? What do you think it will sound like if you increase the amplitude? Experiment for a bit with these two values to see how they affect the sound produced.

So far, we have seen that a greater amplitude produces a louder sound and makes the grains vibrate more. But what about the frequency of the sound wave. How does it affect the grains?

A greater frequency sound wave results in a higher pitched sound. It turns out that different frequencies can make the grains vibrate in different patterns. The relationship between the frequency and the patterns produced is very complicated and is the result of standing waves. This relationship was first described by mathematician Sophie Germain.

Let's investigate these patterns in more detail.

• Place the drum over your speaker and sprinkle more grains evenly over the top. Play a tone with a frequency of 71 Hz. Set the amplitude so that the grains vibrate without flying off. What do you notice? Do grains all over the surface vibrate the same amount? Do grains in some areas not vibrate at all? Do the grains start to form a pattern? Can you draw a picture of this pattern?
• Change the frequency of the tone to 88 Hz. What do you observe happening now? Do grains vibrate and not vibrate in the same areas as before? Does a different pattern start to emerge? Can you draw a picture of this new pattern?
• Try the following frequencies – 120 Hz, 344 Hz and 787 Hz. Does every frequency form a clear and unique pattern? What sorts of patterns emerge?
• Starting with a frequency of 100 Hz, gradually increase the frequency to 1 700 Hz to see if you can find any other patterns. Draw pictures of any of the patterns that emerge.
• How large can you make the frequency before the pitch of the sound is too high for you to hear? Do you think this is because of your ears or the quality of the sound that the speaker can produce?