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About ctanzio

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  1. Bridge Rocking Motion and Leverage

    That video is a good demonstration of how moving waves can combine to give the appearance of a "standing" wave at a natural mode of vibration, i.e., stationary nodes where no wave action appears to be happening, and antinodes where peak oscillations seemed to be fixed. But there are wave-like disturbances constantly propagating through the plate.
  2. Bridge Rocking Motion and Leverage

    Marty's equation is a good approximation for many materials. The more precise equation also accounts for a material property called the Poisson's Ratio. What might be helpful for a builder is how it predicts the frequency changes of plate modes as one changes different parameters. The equation can be transformed into the following: f = K x t x C / L^2 Here, f = frequency of the mode t = thickness of the plate C = longitudinal sound speed L = distance between "boundaries" of the violin K = some proportionality constant Suppose you are looking at a breathing mode which is an asymmetric rocking up and down between the two f holes. You can raise the frequency of this mode by making the plate thicker or lower it by making it thinner, mostly in the sections where it shows the most movement. You can change the characteristic length of the mode, basically some dimension across the violin's width, by adjusting the plate thickness as one approaches the edges. Making that area thicker will make the length appear smaller, and vice versa. Making the length "smaller" rapidly increases the frequency. Of course, this assumes some sort of plate tuning approach is a useful thing, which is a topic which has been covered many times in this forum.
  3. Bridge Rocking Motion and Leverage

    Hardly "standing". The term "standing wave" is a classic misnomer. Pick a point, any point, on the violin plate. The displacement at that point is not standing still but rather changing constantly, only in a cyclical fashion. Mass is being displaced in a very localized way that causes a change in the stress and displacement fields to "travel" through the plate. It can be convenient to think of it as a wave of kinetic energy. For a standing wave, it simply means that the energy reflects off the ends of the violin in a cyclical fashion that causes the displacement of any point to vary in a regular pattern. This is no different than tapping the end of a beam and measuring the longitudinal sound speed. Mass displaces in a very localized way that causes the pressure (stress) to change in a way that appears to move through the beam. It can reflect off an end and return to the original end that was tapped. It continues back forth until the energy is dissipated by several different mechanisms. This is also a "standing" wave in every sense of the term's technical usage. The SHAPE of the wave is just different from the violin plate only because of the way the energy was fed into the system. In terms of complexity, the violin is a rather simple vibrating system compared to the systems that have been successfully analyzed using experimental, theoretical and computer analysis. Why such analysis doesn't seem to add anything to understanding the violin is because there is no quantitative standard that defines a "good sounding violin". If you ever figure that out, finding an Applied Physicist to help you design a violin to that standard would be easy.
  4. Bridge Rocking Motion and Leverage

    Strictly speaking, concepts of leverage are more appropriately applied to static and uniform motion problems. So some caution is needed when trying to use the leverage concept for energy transfer from a vibrating string to the top plate via the bridge. For most of the frequency range of the violin, the method of transferring energy from the strings through the bridge results in wave lengths much larger than the dimensions of the bridge. The bridge essentially acts as a rigid body until one approaches the first prominent harmonic of the bridge which is around 3kHz. The top plate operates differently. Because it is transferring energy along primarily as bending waves, it exhibits a phenomenon known as dispersion: the speed of the wave is a strong function of the frequency of the wave. This is called the group or phase velocity. This is much slower than the longitudinal or shear sound velocities. Roughly speaking, a 200hz bending wave in a spruce plate might travel around 75m/s with a wavelength about equal to length of the violin. So at any point in time, one would see peaks and valleys associated with such a wave. A 800hz wave would travel at roughly double the velocity of a 200hz wave and have half the wavelength. You can verify this for yourself by considering some of the mode animations posted by David. Find one that has a single peak and valley at any snapshot. Look up the frequency corresponding to that mode. Now estimate the wave speed as the frequency times the length of the violin. Edited for clarity.
  5. Cleat Dimensions for Post Crack

    The left side of the picture is supposed to be a cross-grained pillar. Maybe the camera perspective is confusing. The bottom of the picture is the end of the pillar and you can see the grain running horizontally across the face. The cleats I glued in last spring also had the grain going across the crack, but I glued them slab side down. The web site referenced in an earlier post seemed, to me, to say the grain side should be glued to the plate with the grain going across the crack. Did I misunderstand their directions? I encountered something unexpected when setting up the edge clamps prior to gluing the crack. The plate as it came off the violins did not have the edges sitting flat on a surface. The plate was splayed, like someone had grabbed the outer edges and permanently curled them up. As I applied the edge clamps to secure the plate to a 1" thick piece of plywood, the crack closed naturally so that it took what was probably its original shape as it was originally carved. There was a non-trivial amount of clamp pressure needed to get the edges to sit flush to the plywood. I left the plate clamped in a cool, dry room for about 72 hours. When I removed the clamps, I expected the crack to open and the plate to curl out-of-shape again. But the plate shape did not change. The edges now sat flush to the table while unclamped and the crack barely opened. It is as if all the deformation in the plate had been reversed by leaving it clamped to a flat surface for 3 days.
  6. Cleat Dimensions for Post Crack

    Caution expressed about rubbing mating surfaces together has been noted. I will check the fit after trimming the saddle then reconsider my options. I prepped a cleat stick and counter form as per the Triangle Strings reference. Slab cut spruce to 1/4" (6.4mm) thickness. Trim to a width of 1/2" (12.7mm). Angled width edges to 30degress to make a parallelogram shape. Drew a line on either side 1/4" in from edge to act as a guide to align the cleat with the crack. Made a counter form to keep the cleat edges snug with the plate while glue dried.
  7. Cleat Dimensions for Post Crack

    Brad, yes that picture and post describe the nature of the crack after it is "closed". Jacob, I had a prophylactic cleat installed as you described and it probably stopped the crack from progressing any further up the bout even as it dramatically widened as the weather changed. Before I do anything else I will install a new cleat above the end of the crack, this time paying close attention to the cleat dimensions. Thanks for reminding me of the importance of doing this. To everyone who mentioned the possible saddle issues: I can see now that the purfling and crack at the edge is butting flush against the saddle. So I will trim back the saddle a hair at a time to see if that lets me get the crack closed through the entire length. Chung, some modest rubbing of the crack surfaces together sounds like a good idea once I get the crack to close so it only looks like a hair line. I can see this slightly compressing the crack surface high spots to get a flush fit.
  8. Cleat Dimensions for Post Crack

    The crack stops well short of the sound post area. If I recall from when I first got the viola, the chin rest was clamped onto to top some distance from the edge. The crack started at one end of the saddle where the chin rest rested on the plate. So I guess technically it is not a crack caused by the sound post, but rather one that if it continued, it would pass over where the sound post is typically located to the inside of the upper f-hole eye. The poorly fitted chin rest might have started the crack. The crack passes under the purfling, turns towards the saddle, and proceeds through the edge there. I opened the viola and removed the crappy cleats I previously installed. You can see that the crack stops well short of the sound post area and that the SP area is unmarred. The crack surfaces are very clean, basically raw wood. When I push the crack closed, I get a tight fit along the entire length on the bottom side, but the top has an obvious, but small, gap about 40mm long in the middle of the crack length. No amount of flexing or manipulating the plate can get the crack to close in that area. Do you think a little water in the area might get the wood to swell enough to close the gap?
  9. Cleat Dimensions for Post Crack

    When I looked at the cleats more closely, I can see that three of them had spalling, i.e., a bit of the surface fracture off. It is obvious I thinned the edges too much after gluing them in. The edges where the surface splitting occurred were tapered paper thin. Thus I reaffirm my amateur status. There does not appear to be any "gunk" in the crack. Clean with a firm brush and maybe run a stiff wire through to make sure there is no debris adhering to the surfaces? I like the idea of some sort of counter form on the outside surface when gluing it up as the initial repair had a slight offset that could be felt and even seen if one looked closely. Do you clamp the crack dry and get the surface aligned before pouring the mold?
  10. Cleat Dimensions for Post Crack

    Thanks everyone for taking the time to respond with advice. I will get a some pictures together and post them.
  11. Cleat Dimensions for Post Crack

    The Triangle Strings link was useful. Thank you. It appears that the crack failed in a "cleavage" stress mode. The smallish cleats on the back side acted like hinges. As the viola shrunk in the cool weather the plate flexed like someone grabbed the edges of the bout and twisted them downward. As the crack opened the stress was relieved which made the plate deflect even more. Adhesives can be very weak in resisting these types of loadings. I am thinking wider cleats will resist the bending action that caused the crack to open, and perhaps some modest downward loading of the plate when I reglue it to the garland should add bending prestress to offset the cleavage stress. Or maybe if I reattach the plate in a cool, dry room that would account for environmental shrinkage with no need to prestress the plate.
  12. Cleat Dimensions for Post Crack

    The original crack was a hairline. It was cleaned and thinned hide glue wicked into it, but it amounted to a miniscule amount of glue. The cleats are still firmly glued to the bottom of the plate. There is no cleat failure. Untensioning the strings results in the sound post falling, and the crack presents itself visually as unchanged, so it does not seem to be an issue of a sound post being jammed into the plates causing the crack to reopen. All of these are good points to consider during a crack repair, but if it were possible to rely solely on the glue in the crack to restore the full strength of the plate, then one would not need cleats. So I am still left with the original questions about how experienced repair people size their cleats.
  13. Cleat Dimensions for Post Crack

    Sometime ago, a 15.5" contemporary trade viola came into my possession with a prominent post-side crack from the saddle to about halfway up the lower bout. Since it cost me nothing, I decided to pop the top and have a go at "repairing" the crack. I made some diamond shaped cleats of modest dimensions and glued them inside while the plate was clamped with the crack closed. The crack was barely noticeable after reattaching the top and the viola played surprisingly well throughout the summer and fall. After the cool weather settled in (the practice room can get down to about 60F overnight), I noticed the crack had opened up significantly. I can easily insert a thumbnail into it, although it has not cracked completely through the surface. This makes me think that as the viola shrunk a little during the cool, dry weather, the top plate is under some bending stress which has caused the top of the crack to reopen. After seeing a picture of Jacob's repair of a post crack, I realized that my cleats are dramatically undersized across the crack. Which means the crack was probably not sufficiently stabilized against bending stresses that would cause it to reopen at the top surface. So how do you determine what dimensions to make a cleat? How do you determine how many cleats you need and what the spacing between them should be? Thanks in advance four your help.
  14. Minimum top thickness at sound post

    If you install a cross-grain SP patch, do you then cut the sound post so its grain is cross-grain to the patch or the plate?
  15. Elements of construction and responsiveness

    Dual quad, 396 V8 big block in a '69 Camaro was my first car (too many years ago than I care to remember). When I pushed it to triple digit speeds on the Garden State Parkway, I could actually see the gas gauge move. My sister burned out a cylinder drag racing it by the old stadiums in South Philly. I traded it in for a Datsun 1200. I could drive that orange tin can for month on $2 of gas but the fun factor was zero. I'm sorry. What were we talking abut again?