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About ttonon

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    Chatty concertinist

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  1. My thoughts have swung to free reeds again and it occurred to me that there may be an interesting way to theoretically determine an optimum static offset distance for the quiescent tongue. As most of us here know, the offset is the distance the tip of the motionless tongue stands away from the plane of entrance to the slot below. I’m sure some of the makers here ask, what’s the need for such a theory? There isn’t really; makers get along well without it. But for those of us fascinated by the operational details of the free reed, such a theory can illustrate more of the intricate physical principles by which our musical source works. My interest in this topic was piqued during a discussion on this forum when several of us were postulating just how the tongue starts vibrating. Someone posted slow motion videos of the starting tongue and what struck me was that the first sign of motion of the tongue tip was a minute vibration that slowly grew in amplitude, until the tip entered the plane of the slot opening. At that instant, the amplitude of vibration increased very rapidly. The western free reed has a notoriously slow start transient – the time it takes from the application of pressure difference to the moment in which the musical tone can be considered to be fully developed. In fact, there was a period during the 20th Century when free reed organ pipes were in disfavor, precisely because of that. Typically it takes many tens of milliseconds for the transient. I myself think this feature is a hindrance to the bellows driven version in some musical settings. Perhaps it can be improved by somehow linking the key to an arm that flips the tongue the moment the key is pressed. Such a mechanism might eliminate the sluggish start period of time in which the tip is building up the amplitude of its vibration outside the slot. Apart from the time delay, a short, sudden start transient usually adds color and character to the entire musical tone. When we hear the fully developed tones of many musical instruments, when the start transient has been digitally removed, we can’t distinguish them, for instance a violin from a free reed, or even a beating reed, such as a saxophone, or a string sound from a guitar or piano. A crisp start transient also helps distinguish a musical instrument from other instruments in an ensemble, and it helps distinguish one note from the instrument from another note from the same instrument. The piano is a marvelous instrument with a wonderful, percussive start transit. In my opinion, it’s why it works so well in Jazz, hammering out complicated chords in which individual notes can be well distinguished, much unlike the accordion, or English concertina. This is an interesting, though large topic, and let’s get back to nudging the tongue in order to start speaking. The fact is, when the tongue is in that entrance plane, the static pressure force on the tongue is maximum. Assuming that we have a perfectly made reed with a tongue that perfectly fits its slot, this maximum pressure force is equal to the (static) bellows pressure difference times the footprint area of the tongue. There are no other static pressure forces in the system that can be larger than this, because before that moment, with the tongue still vibrating outside the slot, the static pressure in the air flowing around the sides of the tongue, under the tongue and into the slot is everywhere a little above the static pressure on the underside of the slot. It’s when the static pressure under the tongue equals the static pressure below the plate that the maximum bellows static pressure force is experienced by the tongue, and that occurs when the tongue completely covers the slot, blocking all air flow. This explains the observed very rapid increase in vibration amplitude. At that moment, the mechanism for nudging the tongue changes from eddy induced vibration (explained below) to a more direct and much larger pressure force that acts uniformly over the total top area of the tongue. At that moment of tongue coverage, we can write, during push of the bellows and a rectangular tongue, J = (Pb – Pa)*L*W, where J is total pressure force distributed uniformly over the tongue, Pb is bellows pressure, Pa is atmospheric pressure, L is tongue length, and W is tongue width. The above static pressure description is really only secondary to the offset theory I’d like to present here. However, it prepares ground for good visualization of the physics. My other key observation of the slow motion video start of tongue vibration was that the initial, small amplitude vibration of the tongue – before being forced into the slot – was obviously (to me) the result of vortex induced vibration (VIV), or at least periodic eddy induced vibration. VIV is an extremely well studied phenomenon, being of interest to architects and aeronautical engineers concerned for the potential damage such a process can cause to large, expensive manmade structures such as bridges, buildings, transmission towers and lines, etc. and aircraft, rockets, and the like. Most of us know about the collapse of the Tacoma Narrows bridge, only four months after it was built over Puget Sound, Washington, in which self-induced vibrations shook the bridge to pieces in only a 40 mph wind, causing the death of a pet dog in a car, both of which were never recovered in the 200 foot deep water below. For many such structures, VIV is bad; for free reeds, it’s good, because your concertina can’t speak without it (I think). Two most notable individuals associated with understanding vortex formation are Vincenc Strouhal, a Czech, and Theodore Von Karman, a Hungarian-American. Strouhal studied the inherently unsteady process of vortex formation in the wake of bluff bodies, arriving at well-known correlations between Strouhal Number and Reynolds Number. Von Karman shed (no pun) much light on what are called “vortex streets,” which are periodic formations of vortices in the wake of a blunt body in a fluid flow stream. Depending upon the Reynold’s Number (Re), or for a given geometry and fluid, the fluid velocity, turbulent eddys in the wake of the body form various patterns in space and time. A large regime for Re produces von Karman vortex streets, wherein vortices appear alternatively on both sides of the object, becoming regularly spaced and periodic in time. These periodic structures in turn cause periodic forces on the structures, and when these periodic forces couple to the natural vibration modes of the structures, large amplitudes of periodic structural motions can occur, called “galloping,” or “flutter.” Such vortex streets encompass a tremendous range of scale, ranging from geological scales observable from satellites in the wake of Eastern Atlantic Ocean islands, down to individual blades of grass, and down to our tiniest free reed tongues. They probably also occur in outer space. Notice here that the wake of the free reed tongue doesn’t extend very far (taking “far” to mean in comparison to W) before any turbulent eddies approach/hit the slot. I’m assuming the eddy interaction about the immediate region of the tongue surface is key and that perhaps the slot allows eddies to pass through easily enough not to greatly disturb the picture. The attached figure shows the St vs Re plot attained by Strouhal, around the year 1878. This is a cleaned up plot, eliminating the large number of data points and error spread bars. We make use of this information in our Free Reed Tongue Tip Offset theory. The Strouhal Number is given by St = F*W/V, where F is the frequency of eddy formation, W is tongue tip width, and V is air velocity past the tip. Notice that it’s the ratio of two times, the time an air particle moving past the tip remains in the vicinity of the tip (W/V) and the period time of vortex formation, since F = 1/T, where T is the period. This ratio has physical meaning. For instance, if the time an air particle spends near the tip is small compared to the period, its view, or experience of a forming vortex will be as though the vortex is stationary. Unless it’s trapped in the whirl of the vortex. The vortex, being a whirlpool just like a hurricane, experiences very fast tangentially moving air, while the entire structure moves at a relatively slow rate (e.g., the “eye”). Such a picture explains why St values in the figure are not much above 0.2, even though the motion is unsteady. Normally, such low time ratios in periodic fluid motion would lead to a conclusion that individual fluid packets experience very little unsteady (time dependent) changes, allowing one to view the overall motion as “quasi-steady.” But in this case, the washing machine regurgitation of the packets in the vortex - like Hurricane Harvey did to Houston - keeps the packets in the region of unsteadiness, leading to the conclusion that vortex formation is inherently unsteady. Without vortices, air flow produced by constant pressure difference would cause steady flow. Hence, vortices convert a steady flow into a periodic unsteady flow, which is necessary to start the unsteady vibration of the tongue. The Reynold’s Number is given by Re = W*V/nu, where nu is the kinematic viscosity of the fluid. As I understand it, this expression was first introduced by George Stokes, an Irishman, but it was made popular by Osborne Reynolds, another Irishman. The Reynolds Number is an extremely important parameter in fluid flow, showing up in all kinds of disparate flow conditions. It is usually interpreted as a ratio of forces, inertial forces to viscous forces, and I recommend that interested people check out the wiki page (https://en.wikipedia.org/wiki/Reynolds_number) that explains the progression from these forces to the expression above. This page is useful also because it shows a cartoon video on the vortex street behind a bluff body in fluid flow. It's a beautiful play produced by Nature, and from it, one cannot but help not to make the connection between vortices and periodic structural forces. (This is an example of the www at its finest, and incidentally, wiki asks all of its users for a measly $3 donation per year.) With that background, the gist of the Free Reed Tongue Tip Offset Theory is to first make two important assumptions. 1) the minimum bellows pressure to start the eddies is that static pressure that will hold the tongue tip into the entrance plane of the slot. 2) the dissipation (friction) in the system is small enough to allow a very sharp and pronounced resonance when the tongue is excited by an external periodic force very close to its natural frequency. That last complicated sentence can be greatly simplified by stating that a “high Q” is assumed. Anyone who has studied vibrations or electric circuits should know what that means. Physically speaking, what we are doing here is to assume that, in order to start speaking, the tongue needs to be excited by a periodic fluid force that is near its (first mode) resonance frequency, and that periodic force is the force supplied by formation of periodic eddies in the wake of the air flow passing over the tongue tip. When those frequencies match, we have excitation. Strictly speaking, we are not even assuming a vortex street. We are only using the data from Strouhal, in which he has correlated discernible periodic wake forces, as expressed by F in his expression for St (above). We know that, for Re from about 47 to many thousands, as in the case with free reeds, vortex streets are the most likely outcome, but that’s an added understanding to the starting process details. Continuing, one then looks up the Young’s Modulus (E) and bulk density (rho) for the tongue material, decides on the geometry of the tongue, using W, L, and t, the tongue thickness, and assumes a starting value for a, the tip offset. The rectangular cross area moment of inertia is calculated as I = W*t^3/12. Assumption (1) then allows calculation of the start pressure difference Ps (push or pull of the bellows is inconsequential) in terms of the assumed a and geometry, using a well-known beam formula for a cantilever, fixed at one end, free at the other (where the tip is), and uniformly loaded (as in the case here, with a constant pressure difference). The formula is Ps = a*E*I/(W*L^4). From the calculated start pressure, Ps, one calculates the resulting air velocity for the air moving about the tongue tip, as follows: V = (2*Ps/rho)^0.5. This air flow of course occurs before the tongue covers the slot, and it’s obtained from energy considerations (Bernoulli), not dependent on the particular geometries, passages, and streamlines. Next, calculate the Reynolds Number: Re = W*V/nu Here, we use Strouhal’s correlation in the attached figure, between Strouhal Number, St, and Reynolds Number, Re. The fact that it’s in graphical form breaks complete automation of the calculation. I did make curve fits for this correlation, but I used Excel, and there I’m limited in the number of functional forms. Notice that the graph is a semi-log plot, so the polynomial fits offered cannot cover the entire range of Re. I thus split the graph into three fits, all using a 6th order polynomial. I will return to this shortly. Once we find the appropriate Strouhal Number value for the Reynolds Number calculated above, we can calculate the frequency of periodic eddy formation from: F = St*V/W, which is derived from the definition of St, above. With F now calculated, one compares this value to the actual vibration frequency of the tongue. If the calculated F and the actual frequency differ too much, we then assume another offset, a, and redo the calculation until we get reasonable agreement. Physically, this comparison completes the application of the model, which states that the starting eddy frequency is very near the actual vibration frequency. Returning to the graph issue, I have put in an Excel spreadsheet the entire calculation for a. There’s an input section (material properties, geometry, etc.), a calculated parameter section (I, Ps, V, Re, etc.), a logic (decision) section in which the user selects the proper curve fit for the calculated Re with a simple click, and a final comparative section for the two frequencies. I would gladly email this spreadsheet to anyone who’d like it. A small request I make is that anyone who receives it to please not share it with others, because I’d like to know who the interested people are. Or, if you do send it to someone, please let me know who it is. For that, I thank you. Though regardless, I won’t contact my lawyer over it. As a finer point of discussion, the two assumptions listed above are perhaps a bit contradictory. The second requires a large resonance response, yet the first chooses a static start pressure, Ps, able to statically deflect the tip an amount equal to the offset, a. Considering the fact that any mechanical resonant system acted upon by a periodic force produces vibration amplitudes much larger than the amplitude of deflection that force would produce in a strictly static process, one might suspect that the calculated Ps is far larger than the true Ps. But I think it’s more complicated than that. First off, there is no real Ps operating on the system. It’s a fictitious quantity necessary to estimate a start air flow velocity, and since pressure is the only mechanism here to cause air flow, we look for the minimum pressure that can be defined by the given parameters. The actual external periodic force on the tongue that causes motion is that due to the dynamics of eddy formation. This force is different from a Ps pressure force. The eddy dynamics are of course ultimately the result of the applied static bellows pressure, Pb, but there isn’t a one-to-one identification. For me, at least now, I think the idea may give decent results. Of course, we can add complexity to the model by defining a modified start pressure, Ps’ = k*Ps, where Ps is as before and k is some number less than unity that would have to be inputted. I’d be surprised if anyone would be interested enough in this modification to try it, because it means for the maker to keep track of how well the model works for different assumed values of k. I clarify this for purposes of completeness. From calculations, it seems this model predicts at least realistic values for a, though I plan to investigate it experimentally. Trouble is that my workshops are a mess now, in the middle of major clean up. My guess is that makers – like myself – are so familiar with setting a value for a that it’s done almost by second nature, with simple start trials to check out the setting. But I’m not a maker, and if there does appear that such a theory can be useful in any aspect of this chore, I’d appreciate knowing about it. For me, it was just fun enough putting the pieces together. It gave me a better physical feel for underlying physics, and as far as I know, it’s entirely my own. For instance, I have not come across any hint of it in academic literature on acoustics and vibration. Best regards, Tom www.bluesbox.biz
  2. 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
  3. 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.
  4. 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
  5. 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
  6. 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
  7. 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
  8. 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
  9. 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
  10. 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
  11. 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
  12. ttonon

    Harmonikas Reed Sets And Dimensions

    Hi Sami, Would you please explain the columns labelled c.Nr.No. and # ? Thanks. Tom
  13. 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
  14. 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
  15. 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