Whenever I think of Pythagoras, my mind immediately turns to Pythagoras’ theory on triangles. I was pleasantly surprised when I began reading out from the text book to discover that Pythagoras was so much more than just his theory. I used the Science in the Ancient World as my main source of information, as well as the very excellent ‘Mathematicians are People, Too’ biography book:
Pythagorus: Length and Sound
Pythagoras was very interested in music, particularly with regards to how it worked. In his investigations into how sound was made and what it was which altered that same sound, he was able to intrinsically link mathematics and music.
Our first demonstration was to show how length affected speed. The girls took a large mixing bowl and placed a thick elastic band and a thin elastic band around it a few centimetres from each other. These needed to be untwisted:
The girls plucked the thick elastic band. This gave a specific sound:
Becs then held it at the halfway mark and Abs plucked it again. The sound made was higher:
They then plucked the thinner band:
This gave an even higher sound:
Becs then held the thin band at the halfway mark, whilst Abs plucked it again, creating a higher still sound:
They could see that the thicker the band the lower the note, and the shorter the band the higher the note. I let them play around for a few moments on their simple home made guitar:
Demonstration Using a Guitar
I then took out Gary’s guitar. The strings on a guitar get progressively thinner as you work your way down. The girls played about with it strumming each string:
And holding each string down at the half way mark to see the difference it made to the sound produced:
They both took a turn:
The girls came up with the basic rule of the thicker the string the lower the sound and the shorter the string the higher the sound.
And this is basically what Pythagoras discovered, although he went one step further. He was able to mathematically show that if you pluck a string on an instrument it will give a particular note. If you pinch the string exactly half way down and then pluck again, the note obtained is the same note but an octave higher.
Pythagoras: What is Pitch?
The following demonstrations show that sound is actually vibrations in the air.
The first thing the girls did was to remove both of the ends of a tin can, clean it out and fasten some cling film tightly to one end. They then added some pepper evenly over the surface of the cling film:
Ha ha…let the fun begin! Abigail lay out on the table whilst Becca held the can over her mouth:
Abs sung ahhh at as low a pitch as she could. The pepper grains were observed:
The sound waves came out of Abigail’s mouth in waves. A clump of molecules form the crest of the wave and the pepper can be seen vibrating on the plastic. As the spread out air comes out, forming the trough of the wave, the pepper calms down:
Becca then took a turn:
In contrast, she sung ahhh at a high pitch. As the sound wave hit the plastic, the pepper bounced up and down as before, except this time it was bouncing much faster….so faster, in fact, the pepper landed in Bec’s eyes. Poor thing!
The higher the pitch the more sound waves occur per minute, and this is seen in the faster bouncing of the pepper
She then sung louder but at the same pitch. This caused the sound waves to hit a higher crest thus causing the pepper to bounce higher:
I don’t think my photos do it justice, but the pepper really did bounce higher!
Pythagoras: Why is Length Related to Pitch?
So far the girls had learnt that the shorter the length the higher the pitch, and the higher the pitch the faster the sound waves, but how does this all pull together to explain the why.
Abs and Becs pulled a long elastic band around the top of a chair back. They took it in turns to pluck the band:
Again, I’m not sure my photos show it terribly well, but as the band was plucked it moved up and down, with an obvious bump in the middle. I told the girls to take note of the speed of the band going up and down as well as the sound.
Abs then held the band in the middle whilst Becca pinged it:
Again I instructed the girls to compare the speed at which the band moved and the noise that it made:
From this they learnt that a vibrating string makes sound. The thicker the string the lower the pitch of the sound. The shorter the string the higher the pitch. Also the longer the string, the higher the wave crests and the higher the volume.
Phew! That is a lot to take on and who knows whether the girls will remember it all but I must say it has been interesting to study the lesser known discoveries of Pythagoras.
That said, I really did want the girls to know of the theory which makes Pythagoras so well known today. So I read them a couple of fun màths books:
And that finished our study on Pythagoras for this year.
For more posts on well known scientists do click on the links below: