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The Weird Thing About Strings

A lecture given by Edis Bowden at the 2010 EGTA conference

www.bowdenarts.com

Hello everyone my name’s Professor Ed and This is my assistant Dodds We’d like to share with you some insights on how strings work and how they create the sounds that make up our music. Some of the science behind the art, if you like. Why should guitarists be interested in this scientific stuff?? Wouldn’t we be better leaving all that to the boffins – like Dodds and me?? Right from Pythagoras in 600BC until the start of the romantic era which gave prominence to aesthetics, music and science were regarded as the same subject and were studied in the same department in the universities. So the split is really relatively recent.

Also Dodds and I are guitarists. And speaking personally the more I understand about how strings and sound waves behave the more clearly I understand things like:

What seperates a good instrument from a bad one; why good instruments are so difficult to make and therefore expensive; why my student's electronic tuners keep flipping between E and B say when they are tuning a string; what timbre is; what temperament is; how incredible the human ear is; even why some notes sound good together and some sound bad together.

Furthermore, if we as teachers wish to impart this technical knowledge to our students without them falling asleep we will need some interesting ways to teach it.

So I have researched some things that the youngsters find fun that we can use as vehicles and I’d like to share those with you. This is not a lecture in acoustics but.... Some of what follows contains some ideas from MATHS and SCIENCE!!!!! But don’t panic we have .... Einsteins maxim : make everything as simple as possible but not simpler. We also have red cards. We’ll hand these out and you, the audience, are invited to use these football referee style if I start using long words. So let’s get started. The funny thing about strings is......... ......they vibrate!!

The first experiment demonstrated was a recreation of the early stretched string experiments. Safety glasses on, Dodds!!! This is very dangerous ladies and gentlemen – Don’t try this at home. You pluck the string and look...........it buzzes and goes blurry. The demonstration demonstrates just how difficult it is for anyone, including students, to see what is actually happening to the string. All you can see is a blur. What does that mean??? Isn’t sound about waves??? That doesn’t look much like a wave. What’s going on??? Is that this vibration thing???? Well yes but it’s not very clear is it??

I have one student who told me when she was young she tried to put her finger between the two apparent stings. Clearly we could do with a bit more understanding. Let’s see then. If we pull the string back we can feel the springiness....the stretch. This is the string trying to get back to its natural, shortest length. Just like a rubber band. When you let go it races back to its rest position but over shoots. It is then fighting against the springiness and so it gets slower and slower until it stops ....rather like a ball thrown up in the air – demonstrate.

Another example of this type of behaviour is the ball in the bowl, or a cyclist in a valley. Here gravity plays the part of the springiness of the string We can also see it happening with a spring and a weight.... Here is a good internet link showing it....

(Good graphic of SHM in a spring. You can find very similar things for your i-phone if you have one. The app is called Touch Wave).

http://www.youtube.com/watch?v=eeYRkW8V7Vg&NR=1&feature=fvwp

Youngsters might find that a bit boring so here’s one that’s a bit more exciting This website demonstrates these principles on a virtual string and allows you to experiment

http://www.falstad.com/loadedstring/

Lets try ramping the damping up. What is dampening – for guitarists its the energy sucked out of the string through the bridge and into the air as soundwaves with each vibration. Now we are getting somewhere...that actually looks like a wave. Now time for a thought experiment.. Dodds – could we have the thought experiment please.

Imagine we have a pen tied to the string where we pluck it and imagine we can get the paper to roll behind it while the string vibrates we can see what happens in time. Let’s show them, Dodds. A long sheet of paper (such as a roll of wrapping paper or wall paper) is wrapped around a white board and pulled at a constant speed by Dodds while the Professor describes the acceleration and deceleration of the string using a pen to produce a trace. The experiment is then repeated with the string (pen) moving faster to demonstrate the change in number of peaks and troughs per unit of time e.g. second This experiment is a bit difficult to carry round but it is good fun and a good way to engage students.

Here is a good internet link showing it....

http://www.youtube.com/watch?v=T7fRGXc9SBI&feature=youtube_gdata

Now the correct technical term for this is Simple Harmonic Motion or SHM for short...... .....................what ? no red cards?

These names can be a bit daunting. I only really mention it to help you with further reading and youtube searches. For the nippers we could invent another, less terrifying name; we could call it “waviness”. Now you can see that you can get different waves depending on how quickly the spring vibrates. The quicker it vibrates the closer together are the peaks and troughs. In fact we can characterise the different waves by counting the number of peaks and troughs we get per second. Because the more frequent the peaks the higher this number we call it the frequency. Which, of course, equates to pitch. This vibration of the spring is transmitted through the bridge into the belly of the guitar which flexes and compresses the air inside making the sound waves as alternating high and low pressure regions as we saw with the slinky spring. And so we have a link between the blurry string and the sound waves which we hear.

Lots of things in the universe behave in a very similar way so if we can understand what is going on and find a way to describe it we can extend our understanding into other areas and make prediction about how all sorts of things are going to behave and transfer our understanding across to different phenomena. Similarly if we can explain different phenomena to our students hopefully there will be at least one that they can latch onto and apply by analogy to sound and music.

Here are some examples waves in water go like this....wiggly line Our ball in the valley – if you measure its height above the valley floor at different time. DESCRIBE....wiggly line The air pressure at the end of a flute increases and decreases as a wiggly line (see the Encyclopaedia Brittanica movie). Now a brief technical aside...no red cards but keep those aspirin handy.

Here is one of my favourite examples - Dodds, could we have the clock please? To Understand waves you have to understand circles. To understand circles you have to study triangles Which are fortunately easy.

Imagine the second hand of a clock (minute and second hands removed or set to 3-15). Now imagine a very bright lamp placed to the left and a screen to the right. Here’s a photo of my model. When the second hand is at 12 the shadow on the screen is as long as it’s ever going to get. As time marches on the shadow shrinks until at 3 it is invisible (zero). This pattern is repeated in the four quarters of the clock. The key thing to notice is that the rate of shrinkage is not the same at each second. Imagine we could record the height of the shadow at each second as I have done in the simulation below. It becomes clear that at first there is hardly any difference in height between 12 and 1. But the rate of shrinkage grows and accelerates towards the 3 o’clock position.

This is the classic wave shape of the spring and the string. Here is the simulation I made It is on my website. Here is the more mathematical simulation showing triangles. Now if we could measure the height of the side opposite the angle for each and every angle i.e. time then we could make a look up table and a graph.

Here is an example of the look up table and heres the graph. Essentially, a pocket calculator does this.. if you enter an angle and ask it nicely it will tell you the answer..........It basically has a built in look up table. The only thing is you need to “parler” calculator. You need to know the word on the button and the word is SINE. And the waves are called SINE Waves. It is a four letter word but it is NOT a dirty word. It is our friend as it unlocks this huge library of knowledge.

Ok. Does this have anything to do with real life or is this just boffin speak???? Well here is a real life example which I think will appeal to youngsters. Show Tacoma narrows video.

Tacoma narrows bridge http://www.youtube.com/watch?v=P0Fi1VcbpAI

The key thing to look for in the video is that only the central span vibrates. This is because the wind is exactly the right speed to create waves in the road platform that are exactly the right frequency to fit perfectly into the space between the two bridge pillars. This then allows the wind to feed the wave and it grows in size (amplitude). This is a good one to pull out when they ask why when one guitar in the room plays the other acoustic instruments in the room start joining in all by themselves. I you want to do further youtube searches for this look under sympathetic vibration. Students also like shouting into their guitars to make them buzz which is essentially the same phenomenon and also the same as the Tacoma narrows....get the frequency right and it will ring like a bell.

This is the same phenomenon as the soprano shattering the wine glass by singing at a pitch precisely matched to the dimensions of the glass. James – could you assist us with a demonstration We need a volunteer from audience to verify no cheating by putting their hands on the guitar to feel the vibrations (kids love this and it engages them).

James sings C - no vibration. James sings G or F# or something close (dependant on the particular guitar) and we get vibration because it is natural for the guitar to vibrate at that frequency. Just as it was natural for the Tacoma narrows to vibrate at the frequency generated by the wind on the bridge.

This short video illustrates the concept of sympathetic vibration

http://www.youtube.com/watch?v=t5qHWK9jgno&feature=related

When you watch the video notice that one pendulum is the same length as the big pendulum and so its swing gets fed by the big pendulum whereas the others have strings of different lengths and are not fed and never really get going. This one pendulum swings in sympathy with the big weight; they’re buddies. We have seen some examples of waves and we know that sound waves are waves but what about strings? Is all that blurriness in the strings really waves??

Well here is a video of a double bass which shows it clearer than anything else.

http://vimeo.com/4041788

So they are real after all. Let’s see if we can see some sound waves and check that they look nice and wavy. Well I have an oscilloscope on my i-phone and another one on this laptop so lets get a nice note Let’s see if we can get a nice smooth wave from this tuning fork. Note: I have found it difficult to get a PC software oscilloscope for my new computer. Winscope used to be excellent and may still work on older PCs. For mac users I have been recommended Mac The Scope. For i-phone users I can recommend the app Audioscope is very good. When a tuning fork is struck it is very difficult for the students or anybody else to see what is happening.

This nice video uses slow motion to show what is happening

How a tuning fork works http://www.youtube.com/watch?v=pANIvSh2r2A&feature=related

At this point Dodds gave a talk on his collection of tuning forks and the history and development of the tuning fork. We also tried putting one tuning pork from an identical pair in the freezer overnight and one in a mug of hot water and then listening to the difference in pitch. Sadly Dodds and I and the audience could not hear any difference.

However, as Lord Kelvin said, no experiment is ever a failure you always learn something. In this case, although we didn’t get the result we wanted, we learnt that all the fuss by the committees defining orchestral pitch about having the tuning fork at the right temperature to the nearest degree Farhenheit is a lot of fuss about nothing.

I have tried on many occasions to use a tuning fork to make wave on the surface of a glass of water. It has always been very disappointing. We need high speed cameras to see what is really going on.

Tuning fork in Water http://www.youtube.com/watch?v=3qtnbifHKXU&NR=1

This film allows you to actually see how the tuning fork makes waves. I think this fascinates kids: that you can actually see sound (approximately). However these waves are on the surface of a liquid. Sound waves in air are of a different nature. They are waves of alternating high and low pressure that travel out from the source and cause the ear drum to vibrate in (high pressure) and out (low pressure). The rise and fall of the pressure at a point goes as a sine wave You can use a slinky spring to show the two types of wave.

This Encyclopeadiea Brittanica film shows this and other things very clearly.

http://www.youtube.com/watch?v=cK2-6cgqgYA&feature=related

We need a volunteer from the audience to play a guitar note into the microphone and oscilloscope and to Sing into microphone. They love Seeing their own voice on oscilloscope and it really engages them. But......... Oh dear that looks a bit spikey. Thats not the same thing as those nice smooth waves they tell you about in science class and that we saw on the oscilloscope for the tuning fork at all. What’s going on???

Well, instruments are complex things. Every dimension gives rise to its own frequency. If we add them together we get a soup of frequencies which make up your average musical note which looks like that. This is basically...timbre. Lets break it down. What happens when two waves meet. The high bits feed each other to make very high bits and vice versa and so the waves amplify each other. If two waves meet the bits that are pushing the water up coincide with the bits pushing it down then you get flat water. Basically adding the two individual numbers for the heights of the waves together to get the combined answer.

This video shows a nice demonstration

http://www.youtube.com/watch?v=Xqo6sEt1cUE&feature=youtube_gdata

I have a simulation programme that allows you to mix different waves together to experiment and learn. I will try to put this in a form that you will be able to download from my website. The thing that blew my mind with this is that by adding together smooth, sinewy waves you can make a square or a triangular wave or in fact any shape of wave that you like. I will attempt to put some examples of this on my web site in the near future. Here are some videos of it actually happening in water. This is basically how synthesisers and programmes like Sibelius create authentic-ish sounds. The more waves we add into the mix the closer we can get to the real sound; the real timbre of the instrument. This is perhaps what instrument makers do. They work to get the right mix of lengths and thicknesses in the body of the instrument to give the right mix of sine waves to give a nice timbre. Shave a bit off here...sand a bit there so that the dimensions match the resonant frequencies that they want to accentuate.

If you want to look further into this subject it is named after its inventor......Fourier Analysis. Again its timbre. By this point in the lecture hardly any aspirins gone.

This next video shows waves bouncing of the ends of a string (the bridge and nut) to create standing waves.

http://www.youtube.com/watch?v=MT7EpS4OX3k&feature=related

Standing Waves

http://www.youtube.com/watch?v=75bHcNPz2e0&feature=related

Extension to 2 D surfaces e.g. water Soap bubble

http://www.youtube.com/watch?v=oXgPMA1ztNQ&feature=related

Show membrane model.

C:\Users\Edis\AppData\Local\Temp\Temp1_membrane.zip\index.html

If we invest a bit of time getting our heads around the idea of the clock and how all the triangles it makes at different times can make the look up table of the SINE and the sound wave and how you can add waves together to make new waves. Then you can get an understanding of many things: Triangles and circles; you also get for free an understanding of how.to measure the height of tall trees and buildings, without having to hold a tape measure up against them; Map Reading and navigation; Sound Waves Waves in liquids; Radio waves; Quantum Mechanics (well some of it anyway); String theory .

And there’s so much more we’d like to share with you like this vibrating plate expt.

http://www.youtube.com/watch?v=GtiSCBXbHAg&feature=related

MAYBE ANOTHER YEAR!! The beauty of this is there is always something new to be discovered And so we leave you with this video to whet your appetite and a further reading section with more links.

http://www.youtube.com/watch?v=3zoTKXXNQIU&feature=related

Yours faithfully,

Professor Ed (Edis Bowden at www.bowdenarts.com ) And Dodds (Anthony Dodds at www.capriol.co.uk )

The Weird Thing About Strings

A lecture given by Edis Bowden at the 2010 EGTA conference

Further Reading