Jump to content


  • Posts

  • Joined

  • Last visited

Everything posted by ttonon

  1. I should clarify. When I hypothesized that higher harmonics in the first mode vibration of the tongue might translate to musical tone, I didn't mean to imply that the musical tone would be the result of only those harmonics. Harmonics associated with sudden changes in pressures and velocities of air motion due to the vibration are indeed a major cause for what we hear, as acoustic models and experiments verify. My hypothesis is based on the fact that different materials seem to sound differently to many listeners, and if that's the case, how else can they be heard? In more detail, it's possible tongue motion harmonics do not directly contribute, but only indirectly, as for instance if the minute motion of the harmonics superimposed on the main sinusoidal motion first affect the chopping of air flow through the slot. So rather than sound emanating directly from the quivering surface of the tongue (which is my hypothesis), that quivering mostly affects the time dependence of the chopping phenomenon, which is really what we do hear. However, whether indirect or direct, these higher harmonics need only make a contribution to the sound, enough so that we can discern it in the musical timbre. For anyone who claims that these tongue harmonics do not affect the musical tone, I ask by what mechanism can different materials affect the sound? I mean between two metals that can be fashioned into geometries having equal levels of preciseness. So Dana, I never disagreed with Benade's explanation, and I'm assuming here his explanation has to do with the mainstream idea that pressure wave harmonics are associated with chopping airflow. My hypothesis simply adds to it, in the growing comprehension of how complicated Nature really is. As an aside, I'm curious whether Benade attempted any explanation for how different materials can be distinguished. When I chastised Johann for spreading false concepts, I didn't mention that higher harmonics of the acoustic reed sound can be coupled to the air in the cavity, affecting the harmonics, and thinking back on it, that may be all he was referring to. But this is a very weak form of coupling, and it's far different from the "acoustic coupling to an air column" usually referred to with such terminology. Dana, I appreciate your explanation of the practical issues involved with different tongue materials and find it fascinating. The scope of any theoretical contribution I can make to the issue is very small, and it's the maker who carries the real burden. In fact, I wouldn't object to anyone describing my suggestion as a flippant remark from a theoretician. Can you please explain further what you mean by "equally stiff at the designated pitch." I recall you explaining that you used a scale to measure spring force of tongues. Do you use that in this process? Again, can you please elaborate? I do hear a difference between Johann's steel and titanium tongues, and to me surprisingly the titanium sounds brighter. This is emphasized while wearing headphones, as Johann suggests. There is a definite preponderance of the higher frequencies from titanium, and I notice that the steel first sounds much more "mellow," until about 2.5 seconds (where you can actually see a slight increase of amplitude on the graphics) higher frequencies ensue, but don't seem to dominate as much as with titanium. I agree that my perception seems to contradict what the frequency spectrum suggests. As interesting as Johann's data is, it cannot be decisive. Important information is left out. Most importantly, what kind of a microphone was used, where was it placed in relation to the reeds, is that relationship the same for both, was the same microphone used for both, what is the pressure level, what are the thicknesses and lengths of the tongues, what is the width and is it constant with tongue length, is there any profiling, etc. All these can have important influences. I'm struck by the very large 5th harmonic. In my experience, it seems exceptional. I notice that around the 6th harmonic, there's a blip that might suggest a slight contribution from the second bending mode of the beam. There's also a blip around the 16th and 17th harmonic, suggesting a third bending mode, however, we can't say for sure because we don't know if the geometry conforms to that of a simple constant area cantilever, for which such conclusions can be made. Additional blips might be contributions to torsional modes, though that's not too likely, but if pressures are high enough, maybe so. Then we have to wonder about the quality of the recording equipment and the software used to calculate the Fourier coefficients. It's clear that theoretically, experimentally, and practically, a full understanding of tongue material would require considerable effort. Best regards, Tom
  2. Greetings again. Here we compare steel to a titanium/tantalum alloy, Ti/Ta 70/30 Beta, which is used in surgical equipment and prosthetics. It interests me, not so much to propose it as tongue material, but because the tantalum increases the density well above the neat material. The modulus is only a third of that for steel, but its density is a little above that for steel, resulting in a modulus-to-density ratio about 0.3 that of steel. We can compare these results to those comparing Titanium to steel and find that the higher harmonic amplitudes in comparison to steel are very much less in the Ti/Ta alloy. The behavior with increasing bellows pressure shows the harmonic amplitudes making up the difference – just what happens in the Titanium/steel comparison; however, since the higher harmonics of the alloy start with such low values, they don’t catch up to those of steel nearly as quickly or as completely as in the case of the neat material. Comparing these plots with the plots for brass/steel, we see an enormous difference. If we can discern an audible difference in timbre between brass and steel, according to these plots, and if our basic assumptions are correct, there should be an enormous difference in timbre between either Ti or its Ti/Ta alloy and either brass or steel. Another interesting outcome in the case of the alloy is that I couldn’t get a convergence with a solution for bellows pressure less than about 2.2 inch w.c. On the other hand, solutions continue further on for the higher bellows pressure than they do for steel and other materials. This might indicate a material that may not be able to play at very low bellows pressures, but may perform better than other materials at the highest bellows pressures. The last plot in these calculations show that the trend of increasing harmonic amplitude with bellows pressure continues for even the highest bellows pressures, for those above solutions for steel become impossible. We can make such plots for most any feasible tongue material, though at some point, the usefulness tapers off, at least if we are in search of a practical tongue material. The theoretical interest continues, as a way of getting a good intuitive feel for the effect of material properties on musical tone. At this point, I think we need wait for experimentalists to compare information they have from work already accomplished or from new work. There might be other materials I'd like to do calculations on, such as glass, and other geometric factors, such as tongue thickness and plate thickness. A docx file showing these plots are at: https://app.box.com/folder/79305691686 Best regards, Tom
  3. Hi Johann, I was maybe not clear enough. I respect your conclusions on observation and I'm eager to hear about them. It's when you try to explain the physics behind them that I sometimes cannot follow, and it's in the latter area where documentation would help. Best regards, Tom
  4. Yes, that definitely looks like brass to me. Thanks. Tom
  5. That's a bit surprising, though keep in mind, with the lowest frequencies, even a minor interactive effect with anything can cause a pitch change. For instance, around 30 Hz, a change of only one Hz corresponds to a semi-tone. There are other things that change pitch besides acoustic coupling with a resonator. Dissipation in itself always produces a lower resonant frequency than the undamped natural frequency. In the "child on a swing" analogy, with wind resistance, the speed of the swing is reduced, and this lowers the vibration frequency: the period of oscillation is delayed. The calculations I'm doing confirm that dissipation increases with amplitude, due to their nonlinear nature, and show that frequency drops can be as high as 50%! This was a surprise to me. We don't notice such things because we normally cannot excite the reed by means other than an air flow. An experiment that would give us the undamped natural frequency would be to vibrate a tongue in an evacuated bell jar and excite it with a variable frequency magnetic field. Of course, we can also calculate the natural frequency for simple shapes using the Euler-Bernoulli results for a vibrating cantilever, which is very accurate. I'm not saying that you are necessarily observing damping effects, but you may be. When you tell us your anecdotes without providing documents, you can say pretty much anything you want, so from my perspective, I cannot take much of it too seriously, though I'm interested in what your experience tells you. I say that because my interest is more of a scientific nature, and speaking undocumented anecdotes is not science, and I'm sure you understand that. Best regards, Tom
  6. Yes, thanks Wolf. It was a long day. I'll make the correction on the post. Best regards, Tom
  7. Hi Johann, I'm glad to hear that you have the impression that these results are realistic. If you have recordings that can give us Fourier spectrum we can make some quantitative comparisons. One quirk that's interesting is the competition between the 4th and 5th harmonics, something that occurs throughout these calculations, and therefore must have something to do with how the different aspects of dissipation interact with each other and the intermittent pressure forces from the bellows. Best regards, Tom
  8. Hi Johann, if you have recordings of those sounds, it might be interesting to look at the Fourier spectrums and compare them to my results. Best regards, Tom
  9. Hi David, thanks for the info. I can see the color best I think in the second photo, and I agree that the second and fourth tongues from the left are probably not brass. The third is surely brass. Interesting. Tom
  10. Johann, you are spreading erroneous ideas. I believe most of us are aware that the sound produced by the Western free reed is not because the reed is coupled to an air column. This is true for the Asian free reed, an entirely different phenomenon. The Western free reed used in concertinas, accordions, harmonicas, bandoneons, etc, are only weakly coupled to the cavity. There are exceptional instances for the highest pitched reeds, and when that happens, the reed has trouble speaking. In other words, coupling to the cavity is detrimental to the tongue vibration. However, the cavity does affect the timbre of the musical tone. I believe that influence can be categorized as reverberation. Another example of reverberation is to put your ear next to a wall in a noisy room, or to play your accordion very near to the corner of a room. Near a wall, the acoustic pressure amplitude is twice that of the wave traveling toward the wall. This must be the case because the reflecting wave must interact with the oncoming wave so that the particle velocity at the wall becomes zero. The wall is a boundary condition. It stops the vibratory air motion that's part of the sound wave, because the air can't go through the wall. Similarly with the cavity. Sound from the reed strikes the walls of the cavity and rebounds, producing a doubled acoustic pressure (oscillatory) amplitude. The dimensions of the cavity are small compared to the wavelengths of the vast majority of the musical frequencies - all except for the very highest notes. The region of this increased "rebounding" pressure extends throughout the cavity and a little beyond. I know you read my paper describing all this, though others may not be aware of it at: http://www.concertina.org/archive/pica/pica_2005_2/pdf/reed_cavity_design_resonance.pdf Best regards, Tom
  11. Hi Johann, I believe you're under the mistaken impression that I experimentally measured different reeds that I made. This is not the case. I'm presenting theoretical results from a physical model and mathematical solution. The plots I present are the results of calculations from this analysis. If it helps, I present the geometric parameters I used in these calculations, below' Width of tongue = 3/16 inch Thickness of tongue = 0.010 inch Thickness of plate (shoe) = 0.125 inches Length of steel tongue = 1.4 inches Length of brass tongue (same pitch as steel) = 1.19 inches Length of titanium tongue (same pitch as steel) = 2.77 inches Length of carbon tongue (same pitch as steel) = 2.75 inches Best regards, Tom
  12. Greetings again to this series showing results of free reed response from an analytical treatment of free reed physics based on a fluid mechanical model. Titanium interests me because it has close to the same ratio of Young’s modulus to density as does steel, but the Young’s modulus and density are each roughly half that of steel. It thus can shed light on the question whether the ratio of these two material properties is all one needs to make a good educated guess about what a given material will sound like when it’s used as tongue material for a free reed. Others have wondered about using titanium as tongue material, and hopefully, the information presented here can assist in evaluating possible rewards from its use. On the acoustic results, to sum up, no, in the case of titanium, there are important influences on harmonic amplitude caused by individual contributions from modulus and density, and the ratio itself cannot describe all key effects. The docx file linked to below presents instructive plots comparing the harmonic amplitudes of titanium and steel. The results are most interesting in that, for low bellows pressure, titanium harmonic amplitudes are in general significantly less than those of steel, suggesting, if these amplitudes translate to the acoustic sound we hear, that titanium should have a mellower or less bright sound than steel. The prediction is that the sound should be even mellower than that of brass, in comparison to steel. However, as bellows pressure increases, this relationship changes, and the titanium harmonic amplitudes become comparable to those of steel, leading to the conclusion that titanium might sound similar to steel at these amplitudes. At the highest bellows pressure, there are a significant number of titanium amplitudes that surpass those of steel. This is the first example I’ve seen where the character of the sound has such a dynamic nature, with markedly different timbre occurring at high bellows pressure. In previous postings in this series, we’ve seen that brass should sound mellower than steel, with the effect increasing with increasing bellows pressure. Here we see similar behavior, only it’s the titanium that becomes bright, starting from a mellow beginning, in comparison to steel. If this is all true (that these harmonic amplitudes translate to the musical tone), I think it would be advantageous for the timbre of the sound to change so much with increasing volume. Such is the case with many other instruments. In general, any aspect of the musical tone that adds complexity to the sound can often be used as an expressive vehicle. Also, the direction of timbre movement with volume - from mellow to bright - is particularly advantageous and natural. Take for example the tenor sax. Low volume notes can be very mellow, with tender association, whereas loud sounds can be plaintive and attention-getting. As with the other documents in this series, the titanium results can be found at: https://app.box.com/folder/79305691686 Best regards, Tom
  13. Hi Johann, what's the confusion? What would you like to know? Tom
  14. Greetings. In my first post in this series, I forgot to mention the fact that in the comparison plots between brass and steel, the tongue lengths are adjusted so that the brass and steel vibration has the same frequency. In my second post comparing carbon and steel, the two tongues have equal length, and in this post, I give results for carbon and steel tongue lengths having the same frequency. The amazing thing in this comparison is that the carbon normalized harmonics are enormously larger than those for steel. I honestly didn’t expect such dramatic results. And they show large difference even for the smallest bellows pressure. For me, this increases my curiosity over what a carbon fiber reed tongue would sound like. Notice also the dominance of the 5th harmonic over the 4th, for all but the lowest bellows pressures. I've noticed before the contentious battle between these two harmonics, and here it's well displayed. The docx file for this case is the same: https://app.box.com/folder/79305691686 Best regards, Tom
  15. Hi Lukasz, please read the following post so that you can get up to date on these details: Not quite. The analysis behind these posts contains a physical model for the forces acting on the tongue, a mathematical representation of that model, and a solution that is periodic. The method of solution admits only periodic solutions. A solution that starts from rest is not periodic. This is a common practice in the theory of vibrations and in applied mathematics. Right now, I'm not interested in a transient solution starting from zero initial conditions, which I believe would be more complex than the one I've done, and may not even be amenable to analytic techniques, as opposed to the numerical techniques now in vogue, of course because of necessity and the availability of fast computers. No it shouldn't, because this is an analysis of solely the tongue vibration. Hopefully I can use this model and apply it to a coupled chamber, but that's something for the future. Can you please explain what DIX reeds are, and maybe give us a picture? Is it similar to the HOPV (High Output Piccolo Voice) technology? Best regards, Tom
  16. Maccannic, that's a reasonable concern, and the question is, how long would carbon fiber last as a free reed tongue? The short answer is, very long (comma is important here). The long answer is that we need to first understand a little about Fatigue Limit and Fatigue Strength. Titanium and Ferrous (Iron) alloys usually have a Fatigue Limit, which is a stress level below which cyclic motion is unmeasurably large. Above that limit, cycling will cause breakage after a number of cycles, typically in numbers above one or ten million. For steel, that limit is roughly 40% of the materials tensile strength. In an analysis I did, it's not too likely that steel tongues will be stressed above that limit, and thus, steel reeds can last seemingly forever. Nonferrous alloys such as brass and aluminum do not have a Fatigue limit, and Fatigue Strength is used to characterize their performance, often with a Stress-Number (S_N) diagram, which predicts the number of cycles to failure for a given stress level. But still, these numbers can be quite large in many applications. Thus, aluminum is a useful material in aircraft construction. Carbon and other composites are a different story. They don't possess a Fatigue Limit, but that doesn't mean their Fatigue Strength isn't high. Carbon fiber composites are usually in the highest performance level here. There are charts that show fatigue cycles going into 10^8 cycles. That would mean a tongue playing continuously at 1000 Hz would last a month, 24-7. In addition, we'd have to calculate just what the stresses are, and if they are not too much compared to the materials tensile strength, the tongue would probably last indefinitely. Another issue is that the performance of composites depend greatly on the direction of the fibers in comparison to the direction of stress, being much weaker in directions across the grain. Thus, I wouldn't make a tongue with fibers running perpendicular to the long axis. For fibers in the long direction, maximum fatigue life can be expected. The story about Rolls Royce and other anecdotes that involve widely different applications aren't show stoppers. The specific application is key and proof is in the pudding. It's true that in general, composites often fail catastrophically, but that's not really a concern here. There may be a concern on how long the tongue could hold tuning. I've read that, near fatigue failure, Young's Modulus could lessen. Here's a quote I got from Quora, by Thomas Moura, M.S. Mechanical Engineering & Aerospace and Aeronautical Engineering, University of CampinasGraduated 2015: "CFRP has a benign behavior in fatigue when compared with metals with fatigue strength around 80–90% of the static strength in tension, compared to below 50% of steel. As noted by other answers CFRP [Carbon Fiber Reinforced Plastic] doesn't has a fatigue limit, however its fatigue strength for a given number of cycles and loading is a lot better than any metal more so if you normalize by the materials density. For instance, helicopter blades made from aluminum have a finite life of 6000 hours for example, where when those were replaced by CFRP ones, they considered to have infinite life, or at least greater life than the airframe itself." For those interested, in 2012 I posted on the reasons why brass tongues break: https://www.concertina.net/forums/index.php?/topic/14533-why-do-brass-tongues-break/&tab=comments#comment-138648 Unfortunately, the attachment for the figures is no longer available. If one is interested, I may be able to find them. Best regards, Tom
  17. Correct. Sorry for the confusion. But my question is what starts it moving “upward”? With that uncertainty, the rest of your explanation loses me. When the tongue is moving upward THROUGH THE SLOT, it cuts off the airflow. Sorry for not being clear. I'm not sure where your confusion is on what causes upward motion. That motion is part of the vibration, as is the downward motion. Tom
  18. Hi Wolf, by “like usual” do you mean at its natural frequency (the frequency you hear when you suddenly release it out in open)? If so, the reason is because the bellows pressure and resulting airflow trigger the vibration at the right moments in the vibration cycle that matches the natural frequency. It’s like when you push a child on a swing. You push at the right time to accommodate the way the swing wants to swing. This kind of vibration is called “self excited,” and is different from the kind when a vibrating system is forced at a frequency different from its natural frequency. With the tongue, about twice the bellows pressure pushes down on the tongue when it’s passing downward through the slot. That’s the right time in the cycle, as with the swing. Any force acting in the direction of motion adds energy to the motion. As I explained, when the tongue is traveling upward through the slot, it’s being pushed at the wrong time, but the pressure there is only the bellows pressure, about half of what it is when it’s pushed in the right direction. The downward push dominates. That's correct. The tongue actually vibrates at a frequency slightly less than the natural frequency, and that's because of dissipation in the system. Actually, there can be large differences between the natural frequency and the vibration frequency, and the model predicts that very well. But those details are too much to get into here. Best regards, Tom
  19. Greetings again to free reed enthusiasts. In this post, I’d like to show results comparing steel to carbon fiber. In thinking about this issue yesterday, I did a web search and found that people are now selling carbon fiber material in thin sheets – for very reasonable prices. This opens the possibility of experimenting with this material as tongue material. Though, I'm sure some makers already know this. I say this because of the very interesting results from the free reed physics model I’m working on. I put up another .docx file showing the difference between steel and carbon fiber vibration spectrum in the same way I showed for steel and brass, and the link is below. The results indicate that the primary material property that affects tongue vibration is the ratio of Young’s modulus to density. In 2012, I posted a survey of materials that one might consider making tongues from, based on the hypothesis that E/rho is the only material property you need to know as a measure of what the musical tone would be. The link is: https://www.concertina.net/forums/index.php?/topic/14568-reed-tongue-materials-a-survey/&tab=comments#comment-138942 and the original table is still available. That hypothesis is valid rigorously only for the free vibration of the tongue, which occurs after the transients have died out when you start vibration by plucking. I didn’t know what effect it would have in forced vibration; i.e., excitation by a bellows pressure. The physical model I now developed shows that there’s an influence by both E and rho separately, apart from their appearance in the ratio. But now with this complete theory we can calculate the effects of E and rho, along with all the other important parameters, and these calculations give support for the simple idea that the ratio is the primary influence. If we normalize the ratio E/rho for different materials using that for steel (divide all ratios by that for steel), we get 1 for steel, 0.497 for brass, and 6.8 for carbon fiber. There’s considerable variation for carbon, but I think this is a representative value. I’m assuming here that steel sounds brighter than brass, as reported. I assume further that the reason is because steel has about twice the ratio E/rho that brass has. This is true IF the character of these harmonics in tongue motion carry through to the musical tone, and the difference in harmonic amplitude is now firmly established. From the plots, we see that carbon, with an E/rho ratio over six times that of steel, produces higher harmonics that greatly dominate those for steel, even at relatively low bellows pressure. In FREE REED PHYSICS – 1, plots show that higher harmonics for steel dominate those for brass at higher bellows pressure. But with carbon vs steel, the dominance is much more, with carbon favored. As the reasoning goes, we thus expect that carbon would sound much brighter than steel, even much brighter than steel sounds in relation to brass. Of course, I could be wrong, and these tongue vibration harmonics don’t translate to musical tone. I’d be surprised because I don’t see any other way that tongue material could affect musical tone. The fact that players report clear differences in the sound of brass vs that of steel strongly indicates to me that plots such as these can lead to an educated guess on what different tongue materials sound like, just from knowing these two key properties. I did simple calculations on the tongue geometry required for a carbon tongue material. Using available thicknesses (0.5 mm and 1 mm), the lowest concertina pitches would require lengths around 4 inches at 0.5 mm thickness for 100 Hz. These lengths are probably too large, and thinner sheets would be required for shorter lengths. Perhaps the 0.5 mm size could be sanded down. Carbon is a material very easy to work with. The high end is more accommodating, requiring lengths around 5/8 inch at 1 mm thickness for 8700 Hz. A 1 mm thickness is also much thicker than existing steel construction, and that might introduce interesting issues with such short lengths, perhaps in connection with the plate thickness. We can of course now use the model for calculations involving different plate thickness. Another alternative is to make tongues at the extreme pitch ends out of steel. Of course, we can wonder just how bright a carbon fiber tongue could sound, and I encourage makers to give it a try, if they haven’t already. The docx file for Carbon and Steel is at: https://app.box.com/s/zchj1y5d4l65fttok3n4sofupzx2gsio Best regards, Tom
  20. Hi Johann, thanks. I recall you posting that you felt that there is more to the sound of the free reed beyond the simple sinusoidal motion of the first bending mode vibration. At that time, I thought your concern was the tongue's second mode vibration, and not the higher harmonic contribution to the fundamental of the vibration's first mode. I apologize if I didn't understand you, and at that time, I was unaware that those higher harmonics could play a significant role. I tried a quick search for your posts, but the search engine broke down. If you'd like, we can re-visit that issue in another thread. Best regards, Tom
  21. David, that’s quite a puzzle, isn’t it? And Wolf, the physical model must be able to answer that, otherwise, it’s not a good model. Yes, it’s related to eigenfrequency, which is another word for natural (resonance) vibration, but the eigenfrequency is the result, not the cause, or explanation. The question of just how a free reed vibrates puzzled me for years, and no one I discussed it with could make sense out of it, even university professors. I discovered the key when I developed the model. The crux is that the pressure forcing the tongue downward through the slot is twice the force that retards it during its upward motion through the slot. When the tongue is moving upward, it cuts off the airflow, and the pressure force opposing its motion is essentially equal to the full bellows pressure difference. The interesting thing is what happens when the tongue is moving downward while it’s in the slot. Just before it enters the slot, the airflow through the slot is near maximum, because the tongue didn’t yet stop it. That airflow has momentum, and when the tongue covers the slot, the airflow collides with the tongue, converting its momentum to static pressure. This is the same phenomenon as “water hammer,” and the analogy is apt because air at those small velocities is incompressible, about like water is. This “dynamic pressure” on the top surface of the moving tongue adds to the static bellows pressure. Now, since the airflow through the slot is originally caused by the bellows pressure (difference), its kinetic energy has the same magnitude as the bellows pressure (potential) energy. This dynamic pressure adds to the actual bellows static pressure, so the total static pressure pushing down on the tongue is twice the static pressure retarding the tongue’s motion upward through the slot. After I first saw this, I looked for experimental or theoretical confirmation and found it in a paper by Ricot et al, which I posted here a few years ago. Ricot did not analyze the tongue motion, and was concerned with the acoustic sound field produced by the motion, which he did a marvelous job of representing. But both his theoretical and experimental data shows this water hammer effect, and the interesting thing is that he didn’t recognize it. So I’m happy to announce to the world here on our forum the basic physical reason how the free reed works. I hope it’s not a blunder, because my ideas have not yet been subject to peer review. It would be too much to try to present the details of the physical model here. I hope to publish it in the coming months and interested people can read about it then. I will mention that a valid model must give an accurate energy audit in the vibration. The results show a 100% balance between the net energy put into the motion by the bellows pressure and the energy dissipation due to frictional forces. In reality, some of the bellows pressure energy must go into the acoustic field, which is not part of the model. However, the acoustical energy produced by the vibration is a very small part of the energy audit, I think. That reminds me, I have to verify that. Best regards, Tom
  22. "It is my understanding, but I cannot recall from where this was sourced, that if a length of metal is reduced in size along its length and heated at one end, the reduced section will get hotter than the non-reduced section because more heat is carried through the reduced area. If I am correct in this, the the thin belly area of a reed will get hotter than the reed tip if it is thinner in cubic cross-section than the tip, but I could well be wrong, as I cannot remember the source. But this is why I use a heat sink, just in case." David, from how I understand what you mean, you are wrong, unless the Second Law of Thermodynamics is wrong. When the tip of the tongue is heated, there will be a monotonic decrease in temperature down to the riveted end, and heat will flow in that direction, as well as outward to the surrounding air. If the belly of the tongue would get hotter (higher temperature) than parts closer to the tip, heat would flow backward, against the Second Law. Heat flows down a temperature gradient, like water flows downhill. I do however think it's safer to provide a heat sink, because of the annealing affects of elevated temperature, as you mention. In my edit, I add: The idea that "more heat is carried through the reduced area" is erroneous. Heat flow is determined by 1) the conductivity of the material, 2) the temperature gradient, and 3) the cross sectional area of the part. All three of these are multiplied together. With a reduced area, less heat flows, restricting the heat flow that tends to cool the tip. If you maintain the same total heat flow with the soldering iron, the consequences are that the temperature of the tip increases, increasing the temperature gradient, and increasing the heat flow through the thin section so that a new equilibrium is reached. It's the same with water flow in a pipe a reduced section of pipe does not carry more water flow, it only serves to increase the pressure upstream of the restriction. Tom
  23. "I believe 'brass' reeds are really phosphor bronze." David, I'm interested whether this is true. If anyone else can provide reliable information, I'd appreciate it, because I just posted a file that shows calculations comparing brass and steel tongues, and I assumed brass reeds are the common alloy 260 brass. However, there's not too much difference in the pertinent material properties between brass and phosphor bronze, though I should know what the true situation is. Thanks. Tom
  24. Greetings Free Reed enthusiasts. I posted here about a year ago explaining an analysis I was undertaking on how the Western free reed works, starting from fundamental principles in Fluid Mechanics. I’m happy to announce that I’ve made progress to the point where resulting calculations reveal much about the physical working of this sound source, and I’d like to present some results here. Very briefly, the analysis starts with the Euler-Bernoulli wave equation for the vibration of the tongue and combines it with a physical model that describes the external forces acting on the tongue. These forces include the bellows pressure force, the viscous friction acting on the skin of the tongue produced by relative air flow, the aerodynamic “form drag” acting on the tongue, and the effect of the mean airflow through the slot. The model does not include inertial forces caused by air on the tongue, though it can be shown that these forces are small, especially if the vibration frequency is not too large. There are many different characteristics of this vibration, far too many to present here, but without getting into too much background or detail, I can present some interesting results. Many concertina players say they can hear a difference between the sound of brass tongues and steel tongues, and many of us have wondered how different materials would sound. In the case of Brass vs Steel, I uploaded a .docx file that viewers can view on a cloud storage site, with details below. This file contains harmonic amplitudes plotted on a log scale, in the same way that a Fourier spectrum is viewed. The amplitudes are normalized with respect to the fundamental. In order to understand what these harmonics are, consider first that the vibrating tongue can vibrate in different bending modes, each with its own frequency. All free reed vibration in musical instruments involve virtually only the first bending mode, in which the tongue bends in a smoothly curved fashion, with only one node, where vibration is zero, at the rivet. The fundamental frequency of the musical tone we hear is the same as the frequency of the first bending mode, also called a fundamental. These details are sometimes confused. The second bending mode, which can occur under spurious conditions, has a node at the rivet and a node roughly a third of the length away from the free end, and the tongue bends in snakelike fashion. Unlike a string, whose modes of vibration are easily excited and are spaced at frequencies that are closely integer multiples of the fundamental, the second mode of the tongue vibration is roughly six times the frequency of the first mode, with succeeding modes separated by growing frequency gaps. Now, within a given mode of vibration, the tongue can also vibrate with frequencies that are multiple integers – harmonics - of the bending mode frequency. Let’s focus on a tongue vibrating in its first bending mode, the usual case. Let’s also consider an isolated tongue, without the slot, vibrating as a simple cantilever. If the excitation is “gentle” enough, or when any initial “complicated” vibrations die out, the motion will be very close to that of a sine wave. This is why tuning forks sound so pure. However, when the tongue is placed over the slot and pushed by a bellows pressure, the excitation is not so gentle. The external forces on the tongue during its vibration change suddenly, depending where the tongue is in its cycle. These sudden, changing forces induce harmonics in the general motion, although compared to the fundamental motion, they are usually small. You can imagine, instead of the relatively gentle sinusoidal swinging, sudden minute lurches and hindrances superimposed on the motion. Although these adjustments are relatively small, they can be measured, and who can really say how much affect they have on air vibration, and thus on the sound we hear? And if you think about it, how else could brass make a different musical tone than steel, if not by the way it vibrates? We expect that somewhere in the frequency spectrum of the tongue motion, there are clues to why brass and steel sound differently. The plots in the .docx file compare the harmonic amplitudes of tongue motion between the usual ASTME 1095 spring steel and Brass 260, characterized only by their Young’s Modulus and density. Each plot is for a different bellows pressure, indicated on the plot. The log scale means there’s a factor of ten in displacement amplitude separating each integer on the vertical scale. For low bellows pressure, the first harmonic greatly dominates, indicating relatively pure sinusoidal motion. The 2.5 orders of magnitude on the plot is a factor of about 316 in amplitude between the fundamental and first overtone. Also, differences between steel and brass are unnoticeable. As bellows pressures increase, higher harmonics play larger roles, and the difference between brass and steel becomes evident. With minor exception, steel often dominates brass in the higher harmonics, especially for the lowest of those harmonics where differences occur, around the 4th or 5th. However, the first three harmonics or so never really show much difference. Because of the relative amplitudes, we are more likely to hear the differences in the 4th to 6th harmonics more than those in the higher harmonics. From these plots we see a demonstration of the “brighter” sound of steel, or the “mellower” sound of brass, with such differences becoming more pronounced at larger bellows pressure. But why does that occur? The answer to that lies in the details of the physical model, to be uncovered by further investigation. In short, it’s due to the nonlinear ways in which energy dissipation acts in the system. The URL for the .docx file is below, and any visitor should be able to view it. I’m not releasing it for download because I intend to publish these results in the future and I’d rather wait for public release. https://app.box.com/s/zchj1y5d4l65fttok3n4sofupzx2gsio Best regards, Tom www.bluesbox.biz
  25. Hi Dana, good to hear from you. To recapitulate, residual stresses are those stresses within a material even when there are no external forces on the material. A good example is tempered glass, where the outside regions of the glass are in compression and the inside region is in tension, and such a state is intentionally produced by cooling outside regions faster than inside. With all internal stresses, there are regions within the material that pull or push on other regions, achieving a static balance between tension and compression. Thus, if some regions near the surface are in a push/pull with other regions, removing a particular outside region – as we do when tuning a reed - leaves no counterbalance to the forces produced by those other regions. With unbalanced forces, the material can deform in some way, until a new state of internal stress establishes itself. Whether we notice such deformation depends upon the internal stress pattern and how much material we remove. I describe all that to support my contention that any tuning on a reed tongue surface that would cause a significant re-adjustment of internal stresses would most likely show up as a change in curvature along the length of the tongue. I can see how such distortion could result in a noticeable change in pitch, particularly by way of a change in offset. And such changes should be immediate. I’ve heard many claims that use of a reed relaxes internal residual stresses, but had my doubts, until I read your description of what happens to reed tongues after grinding. By “grinding,” I’m assuming you mean that a region of the top or bottom surface of the tongue is remove in order to thin the reed in some area. Such grinding is notorious for leaving residual tensile forces on the surface ground. Thus, after grinding, the curve should be towards the side ground? When you straighten it, you exceed the yield stress on that side by stretching it there. Then, when the tongue springs back, it causes a residual state of compression on that side. If, however, the opposite side experienced a compressive yield during your bending, upon spring back, it will wind up with a residual tensile stress on that side. In general, residual compression near a surface is good, residual tension bad. That’s because metals tend to fail in tension rather than compression and such residual tensile stresses will lower the fatigue resistance during cyclic (complete reversal of stress) loading, as in a vibrating tongue. For other applications such as the leaf spring in a car, fabrication techniques are sometimes used to purposely impart a residual compressive stress on the outside side of the bending, even though residual tensile stresses remain on the inside of the bend curve. There, the uni-directional bend cycling is favorable. In the case of the tongue, I don’t think any residual tensile stresses that you leave on the one side when you straighten the strip should cause fatigue problems, simply because they are probably low magnitude. And also because if it were, you would’ve noticed that straightened tongues tend to break. For the same reason, I think that the general statement, “usage relieves residual stress” can be misleading. Firstly, during manufacture, all blue tempered spring steel 1095 is annealed at up around 1400 – 1500 F, which is a cherry glow, and that itself greatly relieves residual stresses. Any residual stress in virgin material is very low. In order for vibration to release residual stress, the vibration must raise stress in all portions of tongue beyond yield stress. The tensile stress imparted by the vibration process alone, however, is below about 45% of the yield stress for all but the very longest tongues, otherwise you would notice frequent breakage. Thus, for a release of residual tensile stress, the residual stress would have had to be about 75% of the yield stress, which is far above any residual stress after annealing. Incidentally, making tongues out of material that hasn’t been annealed, or from material that has an unknown history could be risky because for instance, if there are significant residual tensile forces such that the vibration process increases stresses much above about 45% ultimate yield stress, the endurance stress limit for that portion of the tongue will be exceeded, likely lowering the lifetime of the tongue. It depends upon the accuracy and resolution of the instrument we measure with. I can see that air density has some influence, but whether our ear/brain is sensitive enough, I can’t say. Maybe when I finish my long-going analysis of tongue vibration, I can offer something interesting there. Best regards Tom www.bluesbox.biz
  • Create New...