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ttonon

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About ttonon

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  1. Hi Chris, Excellent! I always hold out that some other academic type might join these discussions, and indeed, I would celebrate it. In fact, I know (of) a few, and I might drop them a suggestion. I have already invited Jim Cottingham, though I haven't gotten feedback on it, and I fully accept that they might not have too much interest. Anyway, that's the reason I sometimes stick in what I think are relative details suited for us academic types. Best regards, Tom
  2. Hi Chris, I suppose we have the usual interaction between a theoretician and an experimentalist. A theoretician might propose an experiment, but the experimentalist sees many practical issues that complicate the issue. This has occurred a lot in acoustics, and as an example, I’m sure you know of the attempts to decide the question whether vibrations in the body of a flute affect its acoustics. A suggestion for experimental insight is to build a metal flute and a wooden flute and see if the sounds are the same, and if they are, since the metal vibrations would be different than the wood vibrations, it suggests that body vibrations are not too important. The experimental difficulty of course is to build both metal and wood flutes to the same dimensions, which is not easy to do. But this is a digression. I would say yes, when we are interested in timbre. As I mention above, it's probably not as critical if we were only interested in duplicating pitch, but this is basically a guess on my part. Since the entire mass of the brass will flow, banging it with a hammer will work harden the material throughout, and filing it will not reduce the bulk hardness. “Free machining” brass should work, and I think most any type of brass would work. Most all brass types come in three tempers: annealed (after heating and slow cooling), half hard, and full hard. Keep in mind that hardness does not affect Young's Modulus, but does affect ultimate strength. For the same length, a steel tongue should have the same pitch as a brass tongue that is 1.41 times thicker (as I calculated above). For a profiled tongue, the profiles in the different materials should be the same, percent wise. If we are talking about using brass on its own merits, as opposed to an investigation into the reasons why different tongue materials sound differently, there are other practical considerations, and we touched on these in discussions on this news group years ago. I refer to two such threads: Why Does Brass Sound Different Than Steel? http://www.concertina.net/forums/index.php?showtopic=14557&hl=%22why+do+brass+tongues+break%3F%22 Why do Brass Tongues Break? http://www.concertina.net/forums/index.php?showtopic=14533&hl=endurance&do=findComment&comment=138688 In the first of these, we discuss why brass tongues may sound different than steel tongues, bringing up the idea of tongue velocity and its effect on higher acoustic overtones. In the second of these, we point out the concept of endurance limit for cycling stress in metals and reason that maximum stresses in brass need to be reduced because of its relatively low tolerance for repeated stress. One way to reduce stresses is to reduce the length of the tongue. With both these discussions we see good reasons why brass tongues should play at lower volume, as David Elliot has pointed out in this thread, compared to steel tongues. I haven’t yet digested again all the posts in these extensive threads, but will probably find it necessary to do so as this investigation proceeds. Hopefully, the complete solution of the fluid dynamical model of the vibrating free reed - as I’m pursuing according to the method I explained above - will provide the answers to most of the questions we have been asking.
  3. Hi Johann, Let's take the examples of steel and brass. Here's the suggestion: [E/Rho]B x (aB)2 = [E/Rho]S x (aS)2 aB = [ (E/Rho)S / (E/Rho)B ]1/2 x aS aB = (2)1/2 x aS aB = 1.4 x aS Thus, make the brass tongue thickness 1.4 times that of the steel tongue, and the tongue lengths, L, the same for both materials. This should guarantee that the modal frequencies of vibration will be the same for both tongues. And again, this should not depend upon how well the complete reed assembly is made. Concerning acoustic sound (timbre), we will have to investigate further into what geometries can be used to impart the same timbre, if possible. But let's go step by step. Notice that the above result probably means that the brass tongue will be stiffer to the feel than will be the steel tongue, or in other words, the spring constant is higher for the brass tongue. This must be because the brass tongue, with higher density, will also be more massive than the steel tongue. The stiffness increases as the fourth power of the thickness (really the moment of inertia), whereas the mass increases only linearly with the thickness. Thus the effect of stiffness overcomes the effect of mass increase very quickly. The higher stiffness for the heavier tongue is needed in order to keep the mode frequencies the same for the two tongues. Best regards, Tom
  4. I apologize for this delayed response to the many interesting comments in this thread I started. I’ve been going out of town and tending to important issues. For those who don’t know, I’m in Complete Response for Multiple Myeloma, a cancer of the plasma cells in the bone marrow. I have medical treatments (infusions) two days of every other week, and they give me headaches and hangover, but I’m not complaining, it’s not too bad. If by chance, anyone else in the group is going through the same thing, I invite you to contact me privately and we can compare notes, even though this disease is extremely variable. Now being able to provide a more energetic description, I must first state clearly that the suggestion I proposed in the OP is really only the simplest theoretical step in trying to understand why different tongue materials might produce different acoustic effects, and I want to correct a sentence in the “Quote” part of that post, which was a misstatement: According to these theoretical considerations, both tongues should produce the same acoustic sound vibration: fundamental plus overtones. The Euler-Bernoulli wave equation for a vibrating bar is the simplest formulation for such behavior, and it is considered very accurate when rotational inertia and translational shear can be neglected, and that is the case if the thickness of the bar is not too great and the vibrations contain only small angles, which often occurs with free reed tongue vibration. Attached is a .docx file that gives the E-B bar equation and the Timoshenko bar equation. I was not permitted to upload this file. Anyone? Shown is the simplest form for the E-B bar equation, which does not include a forcing function (external force, such as a bellow’s pressure), nor aerodynamic drag (friction) terms. Mathematically, it is called a non-dissipative (frictionless), homogeneous formulation, and the utility of it is that it (along with its boundary conditions) provides the eigenfunctions for any type of bar vibration consistent with its underlying simplifications. In other words, the complete solution when you do include a forcing function with friction (the complete formulation) is made up of these same eigenfunctions, which give the axial dependence of the shape of the bar (its curve). The time dependence of the vibration in this complete case is then determined by the time dependency of the forcing function with the complete formulation. Thus, the simple suggestion in my OP will reliably predict accurate frequencies and general axial beam shapes for the fundamental and overtones that are experienced in actual operation (with dissipation and bellows pressure). And it does not depend much on how accurately the tongue and slot (entire reed) is made. However, it cannot give a complete description of the oscillations in air pressure (the acoustic sound) that the vibrating tongue produces. Let’s focus now on the acoustic sound, which is our prime interest. In order to predict a complete description of the acoustic sound of the reed, we need to know how the vibrating tongue motion translates to oscillatory air motion, and this air motion needs to be understood in the near field (close to the vibrating tongue) and the far field (after the sound waves move to a region away from the reed – say to a region that is more than about ten tongue lengths away, which is the sound we hear). With a complete formulation, we will get some information on the acoustic near field, and here, we may be in luck, at least in so far as making conclusions about how different tongue materials might compare in their acoustic sound (volume and frequency spectrum, or timbre). These conclusions would be enabled because of the addition of a forcing function and dissipation terms into the E-B bar equation, and scrutinizing those terms. It’s the same way I suggested in my OP, only now we have more terms in the equation. The boundary conditions (B.C.) remain the same in this complete formulation (fixed at one end, free at the other). In order to accurately determine what these terms are, we need to develop an accurate physical model for the tongue motion, and how this motion interacts with air movement. I developed such a model after I was invited to deliver a paper at the Acoustical Society of America 2017 meeting this last Dec 4 – 8 in New Orleans. I delivered the paper, with the published Abstract: http://asa.scitation.org/doi/abs/10.1121/1.5014394 New Orleans was fun, and this paper is a work in progress. I have completed the physical model and have conjured a mathematical method of solution for the resulting governing equation and B.C. I now have to finish the formal solution - which at this point, is mostly a lot of Algebra - and to perform calculations and graphical results, check agreement with experiment, etc. But because of further travel plans out of the country, work on this project will be put off for more than a month. I’m explaining all this in the hopes that I can convince a reed maker to first take up the simplest suggestion in my OP. By Spring, I should have completed the analysis and could hopefully make some statements about what geometry would be required to cajole two tongues of different material to not only vibrate with the same frequency and have the same overtones, but also to produce the same acoustic sound, if possible. It may not be possible. And of course, it may not be possible to find such simplistic generalizations from only this study, in which case, we would have to rely on an acoustical analysis of the air sound field. But let’s not yet give up hope on the simplest approaches first. I wasn’t sure how to present all this, and I hope I haven’t confused things with my attempted explanation here. I’m glad to answer any questions, if I can. In the coming days, I plan to respond to the comments by others in this thread. Best regards, Tom
  5. Greetings fellow free reed enthusiasts, In another thread, I made the following suggestion, and perhaps it's worth including it in its own thread. In the above, E is Young's Modulus, a is tongue thickness, and Rho is material density. The simplest example would be a tongue with constant cross section vs. axial length: no taper and no profiling. I believe the criteria here apply also to cases of taper and profiling, as long as their axial dependencies are the same for both tongues, but I'd first like to look at the corresponding solution to the wave equation before asserting that here. Best regards, Tom www.bluesbox.biz
  6. Hi Umut, I think I have a much better idea on what you're asking, and let me offer the following. In general, metals have the lowest Damping Capacity of all materials, and of these, from the information I sent you, Aluminum appears to have the lowest. Thus, I would recommend you try making a gong out of Aluminum. Do you know of other people trying Aluminum gongs? Perhaps a serious problem with Aluminum might be its relatively low endurance limit. In order to evaluate this, you need to estimate the maximum internal stresses that the metal would experience as a gong, and at what frequencies those stresses occur. For this, you can consult the circular plate vibration solution that Morse has in his book (as I explained above). With that information, you should be able to estimate the life time of the gong. Important also is the fact that there are many different kinds of Aluminum alloy, each with its own Damping Capacity and endurance limit. Hopefully, you'd get lucky and find a good enough alloy that's affordable. Traditional gongs and bells aren't made out of Aluminum because this metal wasn't widely available until this last century. When it was discovered about 200 years ago, it cost more than gold, and it wasn't cheaply produced until only the last century. Copper and bronze however have been utilitarian for a few thousand years now. It's not correct to conclude that the low tabulated Damping Capacity for glass fiber ( 0.1) means that you can use it in a composite and it will increase the Damping Capacity of the composite. This value must be valid for a single fiber stretched longitudinally, and not for broken fibers immersed in a matrix. Putting any additive (fibers, nanotubes, powders, etc.) into a material will most likely increase the Damping Capacity over that of the material alone. This is because there will always be some relative motion between the additive and the matrix, and this rubbing produces dissipation of energy, heating the material. Making a gong out of separate components should be avoided, because again, there will be relative motion between these components, causing vibrational energy losses. The gong should be made out of one homogeneous material (e.g., Aluminum, or an alloy of Aluminum). I haven't seen much data, but my guess is that thermoplastics, thermosets, and other polymers have more Damping Capacity than metals, because they have long molecular chains that easily distort, using up vibrational energy. If you do find any will lower levels, please let me know. Glass bells and gongs are fairly common in small sizes. Wind chimes, wine glasses, the glass harmonica (the one invented by Benjamin Franklin), etc. all prove that solid glass can be a resonant material. But again, I think that a solid glass gong would perform best, and in order to make one, I'd first talk to a glass worker. Best regards, Tom
  7. Hi Umut, A few ideas: Solid Glass: Has anyone tried to make a solid "tempered" glass gong? You can try casting a circular molten glass shape, then find a way to cool it rapidly over the entire outside surface, before it can cool throughout the interior. Then let it cool more slowly in the interior. This is basically how they make tempered glass, which has the outer surfaces in compressive stress and the inner regions in tensile stress. Thermoplastic: Perhaps a thermoplastic (not epoxy) dome can be cooled in a similar way, resulting in its outer surface in compression and its inner regions in tension? Thermoset plastic: For epoxy, since the cure rate of epoxy increases with temperature, you might first cast the epoxy in a circular shape, then when it becomes firm enough, heat all the outer surfaces uniformly with infra-red (radiative) heaters. This will cure the outer surfaces first. Keep heating (maybe with an adjustment on heat flux) until the inner regions become cured. Best regards, Tom
  8. I'm constantly amazed by the progress being made by enthusiastic researchers, who keep coming up with new possibilities in most any field of science, medicine, and technology - possibilities that we couldn't conceive of only a couple decades ago. I just hope we can turn away from our destructive tendencies enough so that these ideas can come to fruition. Yes indeed, now is the time to start out on a career that can immerse you in such exciting developments - at least for us privileged enough to benefit from the education and wealth that provide the basis for such a fortunate career. Best regards, Tom
  9. Hi Umut, At this point, I'm not sure what you want to do. Do you want to make a gong of concrete, or do you want to make a gong with a minimum amount of dissipation, so that it has the longest ring? If the latter, you might find this comprehensive materials survey interesting: Documentation of damping capacity of metallic, ceramic and metal-matrix composite materials: https://faculty.engr.utexas.edu/sites/default/files/jmatersci_v28n9y1993p2395.pdf Best regards, Tom
  10. Hi Umut, In this thread, we are talking about two kinds of vibrating objects – free reed tongues (also called bars) and gongs (also called plates) - composed of two kinds of materials – metals and concrete. I believe your main interest concerns the vibration of concrete gongs, and perhaps your interest in metallic bars is in order to help you get an understanding of concrete gongs. I point out these differences because each of these special cases requires different theoretical treatment, and one can error by confusing each of them. Yes, in the case of vibrating bars that are homogeneous (have the same material and cross sectional area throughout their lengths), as described by the Euler-Bernoulli governing equation (which works well for the vibration of tongues of the Free Reed), if the ratios E/Rho and the geometries are the same. As a matter of fact, in these cases, the Euler-Bernoulli ( E-B ) equation allows us to be even more specific; i.e., for two vibrating bars of different materials, if the ratio E*k^2/Rho is the same and if the bar lengths are the same, the vibrational response will also be the same. Here, k^2 is the “radius of gyration of the cross section,” assumed to be constant over the length of the bar, and for a rectangular cross section, equals (a^2)/12, where a is the (constant) thickness of the bar. As an aside, this result suggests a very interesting experiment that concertina reed makers might want to try. Make two different tongues of different materials (say steel and brass), with constant cross sectional area and having the same length and the same parameter E*(a^2)/Rho. According to these theoretical considerations, both tongues should produce the same acoustic sound: fundamental plus overtones. My feeling is that, if this conclusion can be experimentally verified, our understanding of the free reed would be significantly increased. For gongs, we are having another kind of discussion, for at least two reasons: 1) materials, and 2) governing equation of motion. For gongs, metals can behave much differently than non metals. For instance, concrete is supposed to have many micro-cracks throughout its interior, and this will affect the “resonant” or decay-time properties of the gong. Concerning the governing equation of motion for such gongs, since they are relatively thick, rotational aspects of small sections of the gong can be important. The Euler-Bernoulli governing equation neglects these rotational aspects, because the thickness of the bar it describes is presumed to be small enough, which is pretty much true. But for gongs, it’s often best to use a more precise formulation, called the Timoshenko governing equation. One main criterion deciding which equation to use is to compare the thickness of the gong to the wavelengths of the acoustic frequencies one is interested in. As usual with acoustic phenomenon, certain “lengths” of the physical system become important, and the major criterion when such lengths become important is a comparison of such lengths to the wavelengths making up the acoustic result of interest. For a vibrating gong, I’d guess that one would be interested in frequencies up to around 10,000 Hz, which is an upper limit to the overtones average adult hearing responds to. Corresponding wavelengths here are about 3 cm, which is probably getting down to the thickness of practical gongs. Thus, one would expect that the Timoshenko governing equation should be used for gongs. An aside here is to notice the difference between a vibrating bar, or the tongue of the free reed, and a gong. For the tongue, the frequency response required need not go above a couple thousand Hz, because it responds to only the fundamental of the music tone. The overtones are produced by the dynamical behavior of air flow. For a gong, the musical tone in the vibration must be able to respond to all the overtones, which occur at many times the frequency of the fundamental. Thus, for a gong, it’s more appropriate to use the Timoshenko governing equation, which is more complicated than the E-B version. I was not able to find a clear way to write (display) these equations here, but anyone interested can refer to Wikipedia. The Timoshenko equation contains not only Young’s Modulus and density, but also the shear modulus, Poisson’s ratio, along with geometry, and all these parameters occur in complex ways. There is thus no simple way to relate gongs of different materials using the more accurate Timoshenko beam theory. However, there is perhaps an intermediate approach considered by Phillip Morse, in Vibration and Sound, a classic text. In this approach, Morse considers a circular “plate,” which is the two dimensional analog of the vibrating bar, which as we have seen, can be represented well enough by the E-B governing equation. This restriction considers only a circular plate (gong) that is fixed at its periphery, although I don’t think this is the usual way to mount a gong. Regardless, this circumferential boundary condition, produces a governing equation much simpler than the Timoshenko formulation. With this “plate” equation, a comparison of different materials can be made in a way similar to that done with the E-B equation: as long as the parameter E*t^2/Rho/(1-p^2) and the gong diameter are the same, the response of two different materials should be the same. Here, p is Poisson’s ratio and t is the thickness of the gong. All these parameters are considered constant throughout the gong disk. Although dissipation is a complicated issue, it must have something to do with the internal molecular structure of the material, and it is very dependent on the kind of material. I think Poisson’s ratio tells us something about dissipation because this parameter is a measure of the relative motion between microscopic elements. An incompressible material will have a maximum Poisson’s ratio of 0.5, and many metals have around 0.2 – 0.3. These values suggest that microscopic elements change volume when stressed, and this suggests dissipation. With metals, different kinds of dissipation are considered, depending how the stress tensor is modeled in relation to it. There are viscous, Coulomb, and hysteretic models, and one can find much description of these on the web. For concrete, a common model for dissipation considers the relative motion between the sides of micro cracks in the material, which interestingly doesn’t degrade the material. This, I believe, is entirely different than the models used for metals, and thus, understanding why bronze is less dissipative than other metals may not give clues as to the dissipation in concrete. It’s my understanding that Bell bronze (approximately 70% Copper and 30% Tin) has been regarded as a desirable material for gongs and bells for over a thousand years or so, and this is based on empirical evidence. I don’t know how much scientific understanding is behind this practice, but the link below should provide you with some useful information (“A micro-structural model for dissipation phenomena in concrete”). I believe additives are introduced into concrete sometimes in order to increase its internal dissipation, as a way to make the material more resistant to earthquakes. chrome-extension://oemmndcbldboiebfnladdacbdfmadadm/https://hal.archives-ouvertes.fr/hal-01194317/document Best regards, Tom
  11. ttonon

    Harmonikas Reed Sets And Dimensions

    Hi Sami, Would you please explain the columns labelled c.Nr.No. and # ? Thanks. Tom
  12. Yes, I see. Thanks. Although the part about the geometry might be worth more thought, concerning the comparison of timbre between two tongues of different materials. A simple experiment would be to make two tongues of the same material and pitch, but with different geometries. Regards, Tom
  13. Hi Dana, from what I read, UHB-20C and 1095 are approximately equivalent (about 1% carbon, 0.25% silicon, 0.45% manganese), so I'm guessing the different properties you're getting in the steel you're using are mainly down to the heat treatment? Hi Alex, from a purely theoretical point of view - granting that sometimes such a view might be too simplified - I don't think so. Both the Young's (Elastic) Modulus and density of both alloys are essentially the same, regardless of their heat treatment. Thus, the ratios of these two properties are essentially the same, and so, I'd expect their acoustic results to be the same, when fashioned into reed tongues of the same geometry. Unless of course the geometries significantly differ, which is possible, since there are more than one geometries that can produce the same pitch. Thus, the material of construction is not the only thing to consider in comparing the sound of two different tongues. One must also consider their geometries, which I suppose complicates the issue quite a bit. Regards, Tom www.bluesbox.biz
  14. ttonon

    Post Wwii Wheatstone Reed Pans

    If I get this right, this is the first time I've seen a crimped-in tongue. The aluminum of the plate seems to be hammered something like a rivet in order to squeeze and hold fast the tongue at its root. Is that correct? If so and because of the low fatigue resistance of aluminum, I'm surprised this kind of fastening doesn't become unreliable after a while. Regards, Tom
  15. Hi Mustafa, I think this gong maker asks some very good questions. Of course, the surest way to answer them would be to build such a gong, so it seems you have an interesting project to delve into. I would suggest first making a small proof-of-principle model, maybe only a few inches in diameter. Make also a brass, or bronze one and compare the performance. I understand that traditional bell metals are a kind of bronze, about 80% Copper and 20% Tin, which produces an alloy with minimum internal dissipation (friction), providing a longer ring. It's understandable to question whether a 60-inch diameter by 3-mm thick concrete gong would shatter. Thus, you'd want a cement mix of maximum strength, so I would suggest a pure cement mix, with a ratio one part cement and two parts sand. Strictly speaking, concrete contains aggregate (small stones), which I think would cause problems, unless they are much smaller than the minimum gong dimension (3 mm). This discussion takes me back to when I was a child. My father was a brick layer, and he gave my brothers and I a few lessons on mixing cement and laying brick. You should probably talk to someone who is knowledgeable about cement. For Portland cement, a 1 - 2 mix gives a mortar with maximum compressive strength, but I don't know about how the tensile strength varies. In your application, I think tensile strength plays much more of a role than with the usual applications. Adding stones (aggregate) to a 1 - 2 cement mix does not weaken its compressive strength, but it may weaken its tensile strength. There is a strong movement now to move away from Portland cement, because its manufacture produces a significant fraction of man made CO2 in the atmosphere. There thus may be other forms of cement appearing on the market now. In fact, you might consider other stone-like materials. In dental work, they use (or they used to use) a substance called "stone" to make cast mouth impressions. This stone, like cement, is a powder mixed with water, though as I recall, it may be much less gritty and maybe even stronger than cement in tension. Finally, with any material you use, since tensile strength is probably important, you might want to experiment with the addition of fibers. These fibers can be metallic or non metallic. If metallic, it should be non-rusting. If non-metallic, you can experiment with glass, aramid, and other plastic fibers used in making the many composites found in industry. This thread has wandered quite a bit from concertinas, and perhaps most readers here would rather we take this discussion off the forum. You can send me a private message if you'd like. Good luck, Tom
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