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Anisotropic is a big word!

Ambitious project for a 15 year old, none of my kids would have an interest in this stuff. Oh, they're smart enough, but not interested in what Dad is interested in. If i started having that conversation with my kids, eyes would roll!

Congrats on having a 15 year old son whose eyes roll minimally when his dad talks about anisotropic properties!

Sorry, can't help you with the rest. I build by feel (in the Torres tradition...).

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Filippo: Not sure if you have the Gore/Gilet books but lots of stuff in there to play around with and no need for expensive gear. From establishing optimal thicknesses for top blanks to getting correct mode frequencies. My fuzzy old gray matter a bit slow trying to get some of it but I'm sure a sharp young mind with your guidance will not have a lot of trouble.
Tom

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You asked for other ideas as well. I've always thought it would be fun (and educational) to make a set of these: http://www.phys.cwru.edu/ccpi/Helmholtz_resonator.html . If I recall, Helmholtz had the originals blown in glass. They could be used to measure (roughly) the contribution of the various partials in the sound of a guitar. (I know we can do the same thing much more conveniently with electronics. Maybe I like 19th century science because it was available to Torres. Maybe I'm just old fashioned.)

On the Chladni plates, I presume you saw this: http://www.youtube.com/watch?v=AS67HA4YMCs&feature=related . Carleen Hutchins' work is worth researching, and Arthur Benade explains things particularly well. Just to make things a little more confusing, this gives some idea of how the whole guitar gets into the act: http://www.kettering.edu/physics/drussell/guitars/hummingbird.html

I've been considering designing some kind of experiment consisting of a tensioned string attached to the center of a flexible membrane top breaking over some kind of saddle in the manner of a guitar in order to show clearly the up-down movement induced by the string vibration. The bridge and string would have to both be exaggeratedly flexible so the movement would be exaggerated and clearly visible. Your 15 year old could definitively demonstrate the inaccuracy of the rocking saddle fallacy once and for all.

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It might be above his head........but since you are already focused on cross grain stiffness compared to long grain stiffness.......maybe he could convert the long dipole frequency to a modulus and the cross dipole frequency to a modulus for cross grain stiffness and find the ratio of cross grain to long grain stiffness. He could use this to predict deflection of the top in a deflection test testing long grain stiffness and another test where the top is turned 90 deg and test deflection across the grain. Then he could calculate a theroetical X brace angle that would make the top isotropic (a simplified version of bracing that doesn't account for tone bars etc.) Then he could re-do the cross grain and long grain deflection tests and see how close he got to achieving equal stiffness along and across the grain.

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Formerly known as Adaboy.......

Filippo,

If you're looking for a tone generator program for Mac, I found AudioTest to be the most convenient. With the cursor sitting over the frequency slider, you can use the scroll wheel on the mouse to change frequency. Changes in 1 Hz increments. Lots more features than needed for this work. $15 shareware with a free download and 90 day trial. Good on OSX up to 10.6.

http://www.katsurashareware.com/pgs/audiotest.html

Checked output with an oscilloscope, and all is good.

Pat

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Marimba keys and resonators are pretty interesting and demonstrate similarities with guitars , cheap and easy. Nodes can be found with some powder, the tubes are a helmholz function, partials are determined by where the thinning takes place.

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My suggestion would be that your son should find the question he really wants to get answered regarding this topic and you can't answer him in depth within less than a day or so.

If Luigi had no "big" questions he is interested in (I am sure he has) and feeling able to find on his own (with guidance) at least a way towards an answer (I am sure he feels able), in my opinion it simply would be a waste of (his) time to do step into a project of this topic (and should find another topic he really is interested in) - but how he could not be interested in this if he has built guitars?

Let him find "his big question"! Make him read some relatively short articles about free plate tuning, about Chaldni patterns on finished violins and Chladni patterns on finished guitars, let him read some controversial opinions about all this. I believe you already have quite a bit of all of this on your book shelf and on your computer's hard disk.

A "big question" will automatically lead to many further questions he will track down one by one, finding answers (not always final answers) and leaving open question too. I bet that documenting well such an investigation, citing the sources correctly and presenting some (maybe not really new) conclusions will be more than impressive. I further am afraid that the hard part for your son will not be to get started with the project but to find a point where to stop!


I think that a bright minded 15 year old will grasp pretty everything except some mathematical stuff which just requires a lot of time (months and years) to get into.
Doing research on hard to understand nomenclature is relatively easy nowadays with our www, and respective explanations could be part of his project (just a "stupid" idea of me, not that I think it would be a must).

Probably Luigi should find his literature as he goes with his project and start with just two or three hints (and a lot of curiousness) and then dive further into things.


...go back to the second and third paragraphs of my answer to your first question (I really mean it).

Last but not least I think that the technical point of view gets too often misunderstood as an alternative to intuitive understanding of acoustical and structural principles. At least for me technique, maths, physics and intuition merge into one when it comes to luthierie. (I am more a repairs man than a builder, and knowing the reaction of some buddy luthiers on my "flimsy" work I guess that without maths many of my repairs would have failed structurally or acoustically, but none of my customers has complained so far ).

Al 's DVD (http://collinsguitar.com/carruth-plate-tuning-dvd) is the best starting point

Filippo, Some of the other posters have mentioned these, but just to reiterate:
"Fundamentals of musical acoustics" by Authur H. Benade, (which is not too mathematical)
Dan Russell's site at Kettering University: http://www.kettering.edu/physics/drussell/guitars/hummingbird.html
Joe Wolfe's site at the University of NSW http://www.phys.unsw.edu.au/music/guitar/guitarintro.html
Thomas Rossing's "The Science of Stringed Instruments" are all great resources which deal in real science rather than the "kitchen table" stuff found in so many guitar books and periodicals.
Paul Falstad has a great site specialising in all sorts of simulations and visualisations for physics generally and much of it is applicable to guitars: http://www.falstad.com/mathphysics.html
There's the "innovations" page on my site which Luigi may like to browse to get some ideas, and then of course there is "the book" which has a lot of both simple and complex physics, and has been bought by numerous academics in schools and universities (at least, that's where I send them off to!). It's real science applied to guitars and covers so many topics that come up on this and other forums.

Something to think about regarding isotropic plates: you need stiffness longitudinally to take the string load. If you made the plate the same stiffness laterally, you'd be way too stiff to be sufficiently responsive acoustically.

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Trevor Gore, Luthier. Australian hand made acoustic guitars, classical guitars; custom guitar design and build; guitar design instruction.

http://www.goreguitars.com.au

I'm 15 like your son, and I did a similar project last year when I was in 9th grade for honors science. It was interesting, but all I really did was study the somogyi book and all sorts of online documents on forums written by people like Al Carruth. It was an interesting project and I got an A because my diction made the report impressive even though I didn't know exactly what I was talking about on occasion....

Yes! I never understood the fascination with isotropism. You want isotropic, try metal. Same thing with tap tone. Aluminum has the ultimate tap tone (beyond Brazilian). I like to think that tap tone matters, but more isn't always better.

Sorry Luigi,
We're wandering a bit. Markus is right.

One of the areas that I did not see mentioned in the discussions above that I believe would be of interest to a 15 yr. old is performing 'bonk' tests on top plates with a computer and FFT software and then looking at the response data, turn it into a graph (Excel) and then using the data to correlate the modes by performing Chladni tests. The FFT will tell you precisely where to tune-in your frequency generator to get the various modes.

It brings the visualization of responses to the next level with the ability to graphically represent the response and decay of the top-plate or even better yet, perform the bonk test(s) on a completed instrument. It is an excellent learning opportunity to actually see the graphically represented performance of a guitar you have built and then perform the same tests on other instruments and compare the results and the actual sound produced when you play each one.

As in all application of science, each set of experiments generates interest and enthusiasm and then leads to more questions. I only wish that I had had the opportunity (and the available equipment) to do this when I was 15!

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Peter

Trevor knows more than I about the topic, but I would guess that author has misinterpreted something.


Often in an analysis, an assumption is made (like isotropy) to make the analysis easier to do, which then means the results from that particular analysis "require" isotropy.

A regular Diff Eq / vibrations book is very unlikely to cover anisotropic plates. Fletcher and Rossing cover orthotropic (a type of anisotropy, for wood) plates -- they say nothing about losing "efficiency" if anisotropic.
http://books.google.com/books?id=9CRSRY ... &q&f=false (page 88)

Overall, I wouldn't suggest relying on the analysis at the JJ URL... it shows a 1 dimensional 2nd order diff eq (simple mass-spring-damper) and tries to apply it to a plate (which is 4th order and 3-D).

Another point of view: if guitars tops were really better as isotropic, we'd all be using plywood or HPL.

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David Malicky

Hi Filippo,

Sure! "The equation for harmonic motion shows that to be an efficient producer of harmonic motion the guitar plates must have isotropic properties". The equation shows nothing of the sort! The equation that Jack shows on his website is actually the one dimensional equation for damped simple harmonic motion and has no term in it that represents “efficiency” other than the damping constant ß. The equation he shows doesn’t have terms in it for long and cross grain stiffness. He should have been using the equation for vibrations of an orthotropic plate, which is given on p4-60 of “the book” (with the solution on the following page) and was first published as “The fundamental frequency of vibration of rectangular wood and plywood plates” by R. F. S. Hearmon, Proc. Phys. Soc 58, p78-92; 1946. I would put a .jpg of the equation up for comparison, but for some reason, when I upload a pic it won’t display (help, anyone?).

“Basically stated, the harmonic motion equations require isotropic plates”. The harmonic motion equations do not require isotropic plates; they’re just equations of motion!

The ring mode appears when a wave travelling from the centre of the plate reaches all boundaries in more-or-less the same time and reflects from the boundary (there can be a variety of conditions on the boundary, free, fixed, somewhere between) and “bounces back” into the plate, thus forming a standing wave in the plate and hence the closed ring which shows the location of a node. This phenomenon is a function of the Young’s modulus of the plate in different directions (which governs the speed of the wave) and its dimensions (which governs the wave’s travel time) and the boundary conditions, which governs the wave’s reflection or transmission, i.e. a lot more than isotropy. Change the boundary conditions (like gluing the plate to the linings) and all the modes change in shape and frequency.

Now, Jack talks about X-bracing. If you fiddle and shave for long enough, you can close the “ring”. It is seldom circular. Meanwhile, what have you done to the ability of the structure to withstand static loads? Too stiff? Not stiff enough? Then there’s the question of fan bracing, which primarily adds more longitudinal stiffness (anisotropy). Can you close the ring on a fan braced structure? Do you need closing bars to achieve that? Should you be free plate tuning with the bridge on? Simplifying massively, the closing bars just bring the edge boundary in somewhat, so could you just leave them out and use the linings? Does this mean that all fan braced guitars without closing bars are “inefficient”?

Without going into all the ins and outs of whether free plate tuning is useful or not, Jack’s explanation invoking “efficiency” and “requirements for isotropy” is hardly rigorous, especially when he’s not even using the right equations.

To me, a guitar top plate has to withstand the static loads, which are largely uni-directional, and result in a toque such that the structure requires stiffness and strength in the longitudinal direction, which is why the grain is always aligned as it is. If you make the structure the same stiffness orthogonally, you end up massively over-stiff. So to withstand the string loads and for the plate to move “efficiently” (loosely defined as a lot of movement for the oscillating load that the strings exert) you don’t need isotropy, which just adds extra, unnecessary stiffness. And remember that closing the ring says nothing about structural requirements.

BTW, if you want a measure of “efficiency”, monopole mobility is not a bad one.

I hope that wasn't too heavy!

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Trevor Gore, Luthier. Australian hand made acoustic guitars, classical guitars; custom guitar design and build; guitar design instruction.

http://www.goreguitars.com.au

Hmmm... great! So an equation requires something. I alway thought it should serve to calculate something. Certainly, calculating vibrations of an anisotropic plate is much more complicated than doing it for an isotropic plate...

I don't believe what I don't understand.

Here's another novelty, brought to us by Jack Johnston:
Source: http://jackjohnstonguitarmaker.com/aboutus.aspx

Good to finally know what Stradivari really did!

Of course, I do not doubt that Jack Johntson's guitars sound better (have not heard them, it's just a matter of trusting him). But also be aware of his disclaimer:
Source: http://jackjohnstonguitarmaker.com/TheT ... terns.aspx

Oh well...

* * *

But rants aside and back to Luigi's (your) "problem" or task:

As far as I understood you want to do (or you want Luigi to do) a research about the usefulness of Chladni pattern testing (records) in guitar making. Chladni patterns are just one way to look at the vibrational behavior of an instrument (or parts of it). There are more ways to do similar but not identical analysis, like for example looking at spectrograms, or measuring sound pressure levels inside the guitar, and more. I am afraid that a full understanding of the meaning of the Chladni patterns implies reading much more than just about them, due to the fact that most (maybe all) serious publications after Chladni don't treat this phenomena (of the patterns) as a "standalone discipline". You (Luigi) will have to go there and read a lot about acoustics to get relatively few pieces of Chladni pattern related stuff. But it's exactly this relation which makes the whole thing interesting and useful.
I'm not sure if you know this: http://www.speech.kth.se/music/acviguit4/
If it's new to you just browse first through it, heading for vibration modes (which is not really the big part of it, but they are given some importance there, and in the end you will have gone through all of it anyway and you will have another piece of the mosaic! )

Another possible line of inquiry is human perception of guitar acoustics. E.g., double-blind listening tests of ~small changes in guitar construction, component selection, playing technique, etc. With the plethora of subjective opinions about the effect of this or that bridge material, finish gloss level, bridge pin material, etc, etc... a controlled study could do a lot of good. Millions of variables to choose from, of course, so Luigi could pick whatever is of interest to him. These can also be tied back to spectral analysis and/or other acoustic techniques. Variables that can be analyzed by modifying 1 guitar are a lot easier to study; else you need many otherwise identical guitars for the stats to work -- but it need not be a reversible modification if sounds are recorded and played back.

The math/physics/engineering requirements drop a lot (though some stats like t-tests would probably be needed), while psychology goes up. The scientific method is even more important in these kind of studies because of bias potentials. A double-blind approach poses some practical challenges, but there are plucking devices to take the player out of it, and recorded sounds can be presented randomly by a computer. ABX testing is a good place to start for null hypotheses--lots of examples from the audiophile community on it.

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David Malicky

If he's interested in working with Chladni patterns, one thing that's useful in gaining an understanding of what you'll see on a guitar top is to start with square isotropic plates. The easiest ones to use for that are expanded styrene beadboard, which you can get at any lumber yard. You can cut various shapes and see what happens to the modes. You can also cut rectangles of wood and try to relate the mode patterns to things like Young's modulus in the different directions.

I've been wroking with Chladni paterns for a long time. They're not 'magic'; there is no magic in this business. There does seem to be a relationship between what the Chladni patterns look like and the sound of the assembled guitar, but it's nowhere near as simple as saying 'closed Ring= great sound'. The pattern shapes do tell you something about the distribution of mass and stiffness within the plate, and there is probably a relationship between that and the tone, such that duplicating the patterns should be a way to get close to duplicating the tone. But there's a lot to this, and a great deal we don't understand as yet.

I do think of the frequencies of the 'free' plate paterns as being a _very rough_ indicator of the stiffness to weight ratio of the top. Assuming the weight is about 'right' then the stiffness will be too if the frequencies are 'right'. Again, not as neat as you might like, but useful in some degree.

Of course, there is no simple way to predict the frequencies of the assembled modes from the 'free' plate Chladni patterns. There must be a relationship, but with all the other variables that Trevor mentions, it can't be anything simple. Then there is the issue of what the frequencies of the assembled modes 'mean'...

There's no need for strain gauges to measure Young's modulus. There's the static "beam deflection method" where you load the beam, measure it's deflection and compute the Young's modulus using the standard beam deflection equation. Or, if you are doing a lot of wood, there's the dynamic method, where you tap the wood, measure it's frequency of vibration and stick those numbers (and a few others, like those you need to compute density) into an equation and it gives you Young's modulus (and density). If there's a lot of wood to do, the dynamic method is way quicker. I've cross correlated results from both methods and the answers come out the same to ~1%.

Either way, much of the work is in the sample preparation. In both cases you need uniform thickness and smooth surfaces, preferably planed. Planed wood measures up as stiffer because the surface fibres of the wood take a lot of the load. These fibres are "mashed" on a sanded surface so add to thickness and mass but not to stiffness and strength. A hand planed surface, on the other hand, has the surface fibres intact. The dynamic test needs panels to be rectangular, too. All of this work has to be done, anyway, if building with the wood, but is quite a lot of work if you're doing a shop full of wood in one hit. (But isn't that what the "apprentice" is for?)

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Trevor Gore, Luthier. Australian hand made acoustic guitars, classical guitars; custom guitar design and build; guitar design instruction.

http://www.goreguitars.com.au

Filoppo Morelli wrote:
"From an experimentation perspective though, Luigi got interested in your assertion early in the video about density in relationship to Youngs Modulus. So he's working on a hypothesis whereby he intends to go through all the top inventory we have and vet out the observation that YM is significantly related to density."

Please be aware that it's only the E (YM) values for deflection _along_ the grain that correlate with density, and then only for _softwoods_, which all have more or less the same structure. 'Compression grain', present in wood near the bottom of large trees, which is characterized by relatively heavy latewood lines, tends to be denser in relation to it's stiffness than most, and wood from high up in the tree may be a bit lighter than the stiffness would predict.

The only thing that correlates at all with cross grain stiffness, as far as I can tell, is how well quartered the wood is.

I would think that so long as your surface treatment and thickness are consistent, then your measurements would be, even if they were not 'correct'. In other words; if you sand all the samples to, say, 3.0mm thick, with the same grit of paper, you'd rank all of them in the correct order for stiffness and density. If you re-did the measurements with the same samples, but now hand planed with a sharp cutter to 2.5mm thick, you'd get somewhat higher E values, and somewhat lower density. The planed values would be closer to the 'truth' for those samples, but no measurement is perfect.

The question then is, what are you making these measurements for? If all you want to do is decide which tops are 'better' in terms of mechanical properties, than all you need is an accurate ranking, and the sanded values should be fine. If you're using the numbers to figure out the absolute limit of thickness that will be just stiff enough to work, the planed values would be better, but not necessarily 'right'. Even then, any good maker would leave a safety factor; make the top a little thicker then the absolute minimum, if only to allow for final sanding. If you're trying to figure out something about the relationship between wood structure and stiffness, and want to develop equations to relate different parameters, you might need to be much more accurate than any home-brew test.

I'll note, too, that these tests are only really accurate if the width and thickness of the pieces being measured are 'small' relative to the length: to get accurate results you need to test long, narrow, thin strips (which can't be made into tops!). 'Poisson's ratio' couples bending along and across the grain, and has to be negligable for the properties not to effect each other. As the long-grain and cross-grain resonant pitches get closer to each other the 'Poisson coupling' changes the straight lines of long-grain and cross-grain bending into 'ring' and 'X' modes (and alters their frequencies and damping, too!) Such strips are not going to be representative of the whole top they come off of: again, you know what _that_ strip does, but maybe the one next to it is different? Once more; no 'perfect' test.

Basically, as per Al. If you want to compare your results to others, I'd go the planed samples. You might get a little less dispersion in the measurements also. If you just want to rank stuff, no problem, just treat them all the same.

The aspect ratio of the samples is an issue as Al pointed out, but it only really becomes problematic when the aspect ratio of the panel approaches the ratio of the long and cross YM to the power of 0.25. When this happens, the node lines of the first bar mode of vibration get seriously curved. If the lines are straight, you tend not to have a problem and the dynamic method of testing still seems to give good results. Chladni testing will indicate whether or not you have a problem, as you will see the curved node lines, indicating coupling between the long and cross modes of vibration.

If wood testing is of interest, there's probably some stuff on Brian Burn's site, (Lessonsinlutherie) and there is also this paper, if you haven't already downloaded it (I've mentioned it a few times, so apologies to those who are tired of seeing it!)
http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PMARCW000012000001035001000001&idtype=cvips&prog=normal (Also downloadable from my site under "about" / "technical"). It deals primarily in the results and insights from testing rather than the testing procedures per se.

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Trevor Gore, Luthier. Australian hand made acoustic guitars, classical guitars; custom guitar design and build; guitar design instruction.

http://www.goreguitars.com.au

Sanded is fine as long as all your samples are either:
- approx the same thickness
- different thicknesses, but all so much thicker than the layer of mashed wood that it is insignificant in the h^3 term.
But, it doesn't work to compare a relatively thin sample with a thick sample: the mashed layer is a substantial % of the thin one, so h^3 will be inflated more than for the thick one.

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David Malicky

One issue with testing panels, such as guitar top halves, is that there can be a lot of other modes besides simple bending ones that can sneak into the same frequency range as the bending modes you're looking for, and cause problems. For example, there's a bending/twisting mode, with two lines across the plate and one up the center along the grain, that can come in somwhere near the crosswise bending mode pitch. This one involves the lengthwise Young's modulus, and a combined shear modulus. When this happens the crosswise mode can look more like a fish: with a rounded 'head' at one end, a pinched in area, and a 'fish tail' at the other end of the plate. Sometimes you'll get two 'fish' modes, facing opposite directions, at different pitches, and not see a 'real' crosswise bending mode at all.

Any time you see 'mixed' modes like that, the frequency and damping data is also mixed. A good example of that is the 'X' and 'O' mode you see on a square isotropic plate. This happens because the 'lengthwise' and 'crosswise' bending modes are at the same frequeucy, and the Poisson ratio kicks in strongly, so that they add up in- and out-of-phase with each other at different pitches. Ideally, the _average_ of the two frequencies is the 'real' lenthwise/crosswise bending frequency, and the _difference_ between them is a measure of the strength of the Poisson ratio of the material. In this simple case, then, you can use the 'distorted' coupled modes to figure out what the 'ideal' mode frequencies would be, and determine some of the material properties. This only works when the 'X' and 'O' modes are perfectly closed, which is sometimes hard to determine. Sadly, it probably doesn't work in cases like that 'fish' mode, because there's more going on than simple bending.

As Trevor says, you use the curvature of the node lines to tell you when another mode is 'too close for comfort'. In these cases, if you really need to know the properties fairly exactly, you will have to change the aspect ratio of the plate to shift the relationships. This can be difficult if you're planning on making a guitar out of the wood later.

Of course, there's _always_ more going on than simple bending (*sigh*). According to one article on wood properties I've seen, by McIntyre and Woodhouse, determining lengthwise and crosswise Young's modulus via the bending mode frequencies only gets you within about 10% of the 'real' values, even in the best of circumstances, because of the perturbations introduced by the other modes. To get closer you need stronger mathematical tools, data on the other modes, and probably a computer.

It occurs to me as I type that the _real_ science project here might just be one on the limitations of measurements, and how you can use various methods to cross-check things and reveal biases to get you closer to that unattainable 'truth'. This would be a great thing for any young scientist to internalize early on.

Ain't that the truth!

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Trevor Gore, Luthier. Australian hand made acoustic guitars, classical guitars; custom guitar design and build; guitar design instruction.

http://www.goreguitars.com.au