Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: varsigma on 06/09/2023 10:51:32
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I did something a few years ago, ok more than ten years, but I haven't been able to explain it and it isn't a thing on youtube yet.
It involved using an old unwound guitar string in a torsion pendulum. I fixed one end by looping the string through the end bead, around a horizontal pipe and pulling it as tight as possible, the other end was tied in a knot around a piece of steel weighing about 2.5 kg, I actually didn't weigh it or bother with the string's gauge.
I checked the fixed end wasn't rotating by fixing a small piece of sticky tape around the string at the fixed end, so I had a way to see any rotation at that small region, and spinning the weight. I attached more of these small '"flags" along the string so I had about ten or so.
To my surprise, and anyone can try this, some of the little flags started rotating in the opposite direction to the weight, then rotating the same way again. This became more apparent as the weight was spun up then released. I did this over weeks of this thing sitting outside hanging from a steel t-bar, the guitar string never broke.
footnote: I was fortunate that the materials, particularly the weight and how it was shaped, were available. The piece of steel would be recognisable to a scaffolder, it was a flat u-shape with a small length of steel pipe welded to the bottom. I lived with some tradies for a while, in Sandringham.
The other essential is a place to hang it that doesn't disturb the peace too much.
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the guitar string never broke.
Well, that's a win anyway!
Seriously, how many turns did you give the weight? If it rotated less than a few degrees in the first instance, you'd expect the resulting torsion to be pretty well linearly distributed up the string, but with a large angular displacement you could see some hysteresis, particularly if it was a nylon string, so some parts might still be rotating clockwise when the weight started to rotate anticlockwise.
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Seriously, how many turns did you give the weight?
A lot. Enough so it would unwind for more than 20 seconds.
I was actually trying to break the string--a steel string, high tensile steel is used in guitar strings--and it was harder than I thought. I wanted to see how much different parts of the string were rotating, expecting to see a more or less exponential distribution. I saw something else, and I repeated the experiment sufficiently that I'd say the result is 3-sigma at least.
To make a torsion pendulum using a high tensile steel string and a weight, you need the weight to be the right shape so it will rotate without wobbling around, the math here is the inertia tensor and the radius of gyration; but you can just choose an object that looks about right instead. Another problem I had to solve was how to attach the weight to the steel string, I had to weave a sort of cage out of nylon twine for a weed whacker around it and tie the string to that. It didn't have to look good, it just had to be a torsion pendulum.
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Hi.
I don't know. Limitations of human vision need to be considered. Are you absolutely certain these sticky-tape flags were spinning in opposing directions?
Compare with "the wagon wheel effect", where any spinning wheel can appear to spin backwards - this is an effect called "aliasing". I'm not suggesting your eye is a camera with limited fps (frames per second), only that your brain is trying its best to interpret the images as a smooth and consistsent motion which may be difficult for something spinning that fast.
Best wishes.
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Are you absolutely certain these sticky-tape flags were spinning in opposing directions?
Yes absolutely. I was quite curious I can assure you. The weight was spinning the fastest, the flags were rotating as the part of the string they were attached to also rotated, all at less than the rotation rate of the weight itself, and in different directions.
Some of the flags would change direction several times as the weight rotated in one direction, The period was quite long, I could spin this thing up about fifty turns or so quite easily. So I had a pretty good window. I could have recorded it on a video I suppose, But as I say, you can try this at home.
One unanswered question is, does this work with other materials, nylon strings, or other metals? Is there something about high tensile steel that gives it this ability to stay, um, coherent under stress?
I guess, having done this a sufficient number of times and observed the same effect each time, I can say I've observed evidence of a steel string winding and unwinding at the same time. Another observation was that this differential rotation was quasi-periodic. That suggests something.
Another footnote: I was actually quite perplexed with this, it was an unexpected thing to find and, I suppose it challenges my concept of continuity. Again I defer to any experimenters out there who can confirm or deny they also observe this behaviour.
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Decorative torsion pendulum clocks are all very well, but I recall being marked down in a physics practical for over-rotating a metre-long torsion suspension: "It all gets a bit nonlinear if you exceed 45 degrees of rotation" said the friendly research student demonstrator who later became a professor. I wish I could remember what we were trying to measure!
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Yeah. I suppose you can add this experiment with one observer, to the set of nonlinear effects of torsion on the material thread.
Ahem. I have tried a similar thing with an ordinary springy plastic length of material, recognisable to people who need to fix their security card to something, secure. In that case the weight was a cheap torque wrench taped to the end of this long stretchy plastic spring--a loosely wound spring--and I was staying at the time in a place that had a projection TV in the lounge so I had the fixed end of the spring hanging from the bracket.
So spinning it up, which means forcing it to rotate well beyond the linear region, like so the plastic spring starts to curl up around itself, then letting it go means lots of angular momentum in the spinning weight, and lots of standing waves in the spring. I did attach a few sticky-tape flags and saw no retrograde rotation anywhere, although the rate of change for each flag wasn't constant either, they at least all went the same way as the weight . . .
Another thing that's occurred to me is that stretching the guitar string with a fixed weight will tune it to a certain frequency, if you pluck or strike or bow the string it will resonate. So does twisting the string affect how the string resonates, or change the frequency? An experiment would need a way to apply the same amount of energy to the string so it emits a tone, you would want to Fourier analyse the output and so on. What you will need is . . . a well equipped lab with an engineering department, commonly found at universities.
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What you will need is . . . a well equipped lab with an engineering department, commonly found at universities.
Or an electric guitar and an oscilloscope attachment for your PC. Unfortunately the really cheap and hugely versatile DrDAQ, used in many schools, has ceased production but there are plenty of devices available for less than 150 pounds and you can have a lot of fun with them!
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This sort of thing isn't the last word in precision but...
https://www.nutsvolts.com/magazine/article/turn-your-computers-sound-card-into-a-scope
https://www.zeitnitz.eu/scope_en
https://scope.software.informer.com/
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I would like to analyse the hell out of any acoustic output from the high tensile steel string, including when the weight is rotating. I also think a way to map the rotating flags to a FT, even to a Laplacian, would be nice. A power curve, say.
Obviously the end of the string fixed to the weight is rotating the fastest and the other end the slowest, so logically there's a distribution of rotational speed along the string when the weight is spinning. Why parts of the guitar string rotate in different directions is the puzzle, it defies logic--but which logic?
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One consideration is that the fixed point at the top may be
rigidly fixed, in which case you can expect any longitudinal signal to be reflected from a node, or
not rigidly fixed, in which case you can expect the support to resonate, store and reflect some energy.
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One consideration is that the fixed point at the top may be
rigidly fixed, in which case you can expect any longitudinal signal to be reflected from a node, or
not rigidly fixed, in which case you can expect the support to resonate, store and reflect some energy.
The problem is where to attach or position a microphone. A pickup stuck to the string somewhere so there's minimal damping.
Otherwise an external pickup for the sound transmitted through the air. Or both. Whatever you do, the pickup/acoustic detector is going to have some effect if it's stuck to the string, wrapping a small strip of tape around a string has some effect too.
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Don't use a microphone - use a guitar pickup, which is what it is designed for! Or use the coil and magnet assembly from an old moving-iron headphone. But any of these, or even a microphone, will only detect transverse vibrations of the string, which are pretty well known to any musician, calculable, and at a much higher frequency than the phenomenon you want to explore - the transmission of torsional movement.
Measuring torsional vibration on physical systems
The most common way to measure torsional vibration is the approach of using equidistant pulses over one shaft revolution. Dedicated shaft encoders as well as gear tooth pickup transducers (induction, hall-effect, variable reluctance, etc.) can generate these pulses. The resulting encoder pulse train is converted into either a digital rpm reading or a voltage proportional to the rpm.
The use of a dual-beam laser is another technique that is used to measure torsional vibrations. The operation of the dual-beam laser is based on the difference in reflection frequency of two perfectly aligned beams pointing at different points on a shaft. Despite its specific advantages, this method yields a limited frequency range, requires line-of-sight from the part to the laser, and represents multiple lasers in case several measurement points need to be measured in parallel.
Not entirely ridiculous: you can extract simple shaft encoder parts from a mouse or a trackball. Given the mass and torque involved in the guitar string/scaffold pipe assembly, a gram of plastic isn't going to upset the motion very much, and as you say the phenomenon was first observed with paper flags.
Which raises another possibility: back to the paper flags, and a webcam.
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Which raises another possibility: back to the paper flags, and a webcam.
I'm short of a few things at the moment. I can find an old guitar string or two, the webcam is covered by my smartphone, sticky tape flags, can do. A place to hang my masterpiece, not a thing yet.
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One of the joys of living in an old barn is the accessibility of the most basic item of physics lab kit - an oak roof beam, replete with rusty nails and ancient bolts. I'm tempted to to the experiment myself!
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It is easier to post the guitar string to the barn than vice versa.
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The barn is not short of guitar strings, but thanks for the thought.
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Are all guitar strings created equal?
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This could be a first in garage physics.
It turns out that violin strings have the largest range of materials. Steel guitar and piano strings are made of high tensile steel as mentioned. Most steel guitar strings are wound with bronze wire. I used an unwound string which was a B or 2nd string, probably light gauge because that's what I usually buy.
I'd like to set up at least two torsion pendulums using different materials and hopefully reproduce the effect I saw (many times) with the unwound steel string; while demonstrating the effect isn't seen in say, nylon twine, or ordinary string.
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What you will need is . . . a well equipped lab with an engineering department, commonly found at universities.
Or an electric guitar and an oscilloscope attachment for your PC. Unfortunately the really cheap and hugely versatile DrDAQ, used in many schools, has ceased production but there are plenty of devices available for less than 150 pounds and you can have a lot of fun with them!
A telephone pickup, a button magnet, and a free copy of Visual Analyser on your laptop would be about the cheapest option.
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I'd like to point out that this weird guitar string thing started out with what I could call a naive algorithm.
It was a used guitar string, it was slightly rusted. I expected the weight itself would break the string if I swung the weight and overstressed the string that way. After many tries I went for as many rotations as I could bother 'storing' in the system by hand, about eighty or so maybe at the height of my enthusiasm, in order to overstress the string. But no breaking string despite hundreds of attempts. I didn't try lifting the weight up and letting it fall, though.
There is something very durable about high tensile steel
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There is something very durable about high tensile steel
What's the tension on the string when it's in the guitar? A lot more than your 2.5kg weight at a guess.
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What's the tension on the string when it's in the guitar? A lot more than your 2.5kg weight at a guess.
I've busted a few steel strings by overwinding them, so that gives you a way to test the durability. At least in one dimension of stress. To make it lab-worthy use a strain gauge; engineer an old guitar somehow.
But I can't help noticing that introducing rotation into the system, makes things more interesting. Although that would be difficult to engineer with an old guitar . . . It is possible to rotate one end of the steel string while the other end is fixed.
Torsion seems to be a more interesting domain than linear stress, for steel guitar strings.
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Are all guitar strings created equal?
Very far from it. I have skinny "cheese cutter" steel top E strings for a folk acoustic guitar, all sorts of nylon thicknesses on my classical guitars, heavy steel jazz strings, plastic coated nickel-wound jazz bass lower E's, and the weirdest instrument of all is a bass ukulele with fat lumps of silicone rubber that oscillate at the same frequency as a tape-wound double bass string four times as long, but still have a useful sustain.
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There is something very durable about high tensile steel
What's the tension on the string when it's in the guitar? A lot more than your 2.5kg weight at a guess.
D'Addario (manufacturer of instrument strings) quote a range of 6 - 12 kg per steel string.
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Very far from it. I have skinny "cheese cutter" steel top E strings
I understand it's traditional to say "thank God it's not a G string".
What's the tension on the string when it's in the guitar? A lot more than your 2.5kg weight at a guess.
It's calculable.
https://en.wikipedia.org/wiki/String_vibration#Derivation
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the weirdest instrument of all is a bass ukulele...
I'm not sure that statement requires further qualification.
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from: vhfpmr on 13/09/2023 12:55:25
What's the tension on the string when it's in the guitar? A lot more than your 2.5kg weight at a guess.
It's calculable.
https://en.wikipedia.org/wiki/String_vibration#Derivation
Reminscent of the Leaning Tower story. The three usual suspects have a barometer. The pilot climbs to the top, measures the air pressure, and calculates the height. The engineer attaches a long piece of string to the barometer and swings it from the top of the tower so it nearly touches the ground, then calculates the height from the period of swing. The cabin steward walks into the ticket office and asks "how high is the tower?"
I refer the hon gent to reply #24 above.
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from: alancalverd on Yesterday at 17:03:03
the weirdest instrument of all is a bass ukulele...
I'm not sure that statement requires further qualification.
Ask anyone who has played one! Great fun, but it's the size of a violin and the register of a double bass, so every note is a surprise.
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every note is a surprise.
I can achieve that effect with a triangle...
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from: vhfpmr on 13/09/2023 12:55:25
What's the tension on the string when it's in the guitar? A lot more than your 2.5kg weight at a guess.
It's calculable.
https://en.wikipedia.org/wiki/String_vibration#Derivation
Reminscent of the Leaning Tower story. The three usual suspects have a barometer. The pilot climbs to the top, measures the air pressure, and calculates the height. The engineer attaches a long piece of string to the barometer and swings it from the top of the tower so it nearly touches the ground, then calculates the height from the period of swing. The cabin steward walks into the ticket office and asks "how high is the tower?"
I refer the hon gent to reply #24 above.
Yes, but won't give you the insight that, if you took a high tensile steel wire and annealed it, then strung the guitar (albeit, a long way from tightly) it would give the same fundamental note as before heat treatment.
The stiffness of the string has essentially no effect on pitch.
(Though, even with my "tin ear" I can expect to tell steel strings from nylon. It's as if timbre and pitch are independent.)
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The stiffness of the string has essentially no effect on pitch.
Instantaneously, true. But IRL the strings creep so you have to retune a classical guitar (with nylon or gut strings) between numbers if the strings are fresh. Steel strings also yield a bit but are easier to stabilise if you have strong fingers - I was taught how by an old dance band pro who reckoned to change a string and stabilise it between numbers. One thing that has improved in the last 70 years seems to be the durability of steel strings - I used to break one every couple of gigs, and now they seem to last until they are too corroded for comfort. (touch wood! I have a gig tonight!)
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What's the tension on the string when it's in the guitar? A lot more than your 2.5kg weight at a guess.
It's calculable.
https://en.wikipedia.org/wiki/String_vibration#Derivation
It is, but if you don't know the unit weight of the string, it's quicker and easier to measure the tension than measure the weight.
The stiffness of the string has essentially no effect on pitch.
In the specific case of a long, thin guitar string the effect of stiffness is negligible, but in general the stiffness does affect the resonant frequency, by an amount that increases as the L/W ratio, and tension decrease. Consider the case of twanging a ruler on the edge of your desk: there's no tension at all, but it's still resonant.
I did a lot of work on this about 10 years ago in the context of using tone to measure the tension of cycle wheel spokes, prompted by the mention of this website (https://www.bikexprt.com/bicycle/tension.htm) on a cycling forum. To clarify: the tone of the spoke is a very quick, easy and accurate way to match the relative tension from one spoke to another, but the formula cited by Wikipedia and John Allen is as much use as a chocolate teapot for determining the absolute tension, and for for a number of reasons.
The first, (not applicable in the case of guitars) is that a cycle spoke has two resonant frequencies, something that's easy to see if you view the tone with a spectrum analyser. The more dominant one is determined by the distance from the nipple to the first crossover, not the spoke length, and the other by the distance from nipple to second crossover or hub flange, it's not really distinct enough to tell which.
The second is spoke stiffness. I measured this error at around 15% at working tension, increasing to 35% or more at lower tensions.
The next is that the calculation supposes the weight/diameter of the wire is uniform, which in the case of butted spokes, it isn't. Since the frequency is much more sensitive to weight in the centre than at the ends, calculation for a butted spoke on the basis of average weight is much less accurate than using the weight at the centre.
Finally, it's not easy to determine the actual length of the spoke, as the first point of contact with the nipple could be either the bottom of the counterbore or the point of entry, and at the other end, the first point of contact is either the periphery of the spoke hole for inbound spokes or the periphery of the flange for outbound, or more likely, the second crossover.
Having discounted any prospect of using tone to determine tension in situ, I built a test rig using a lever to tension one single test spoke in isolation, in order to determine the practicality independently of the error introduced by the crossovers. The plot below shows the error in the tension determined by tone as a function of tension for a the following wires:
Double butted spoke calculated from average weight
DB spoke calculated from centre weight
Plain gauge spoke
A piece of brake cable (stranded and flexible)
A single strand of gear cable
Also marked is the maximum error I can account for by analysis of the test setup.
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The difference between a flexible brake cable and the much stiffer spokes is conspicuous.