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Old 04-13-2017, 04:50 PM
LPMark LPMark is offline
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Default Physics of string vibration

In the quest for best playability, after dozens of builds of acoustic. solid body electrics and semi hollow and countless setups over the years, I have concluded that playability is only partially determined by the fingerboard.

Assuming an ideal fingerboard with level frets, relief or not, the minimum action that can be achieved varies from one instrument to the next.

R Siminoff states in the "Luthiers Handbook" that for acoustic instruments with a FIXED bridge that "little or no power comes from the lateral vibration".
Lateral vibration causes the greatest string excursion and is the limiting factor of how low the action can be and appears to be affected by resonance of the entire system.

Perhaps if the top plate on fixed bridges could be made stiffer to lateral deflection, but decrease resistance to rocking motion by say a modification of X brace/bridge plate structure, playability could be improved.

Doe's anyone have any insight into this?
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Old 04-13-2017, 04:56 PM
charles Tauber charles Tauber is offline
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Paging Alan, who has lots of insight into the issue....
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Old 04-13-2017, 06:29 PM
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srick srick is offline
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There was a Fretboard Journal podcast with Roger where he discussses this in more detail. (I'm sure you can find this on their site) He used these concepts in the design of his "Straight Up Strings" sets. It's a very interesting concept, but I suspect if it was the be-all and end-all in bracing design, someone would have discovered it before this and it would be the standard we all live by. One very interesting analogy he made was comparing the guitar top to a trampoline and the strings to different weight jumpers. Anyway, listen to the podcast for more.

Best,

Rick
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Old 04-13-2017, 07:28 PM
Howard Klepper Howard Klepper is offline
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Quote:
Originally Posted by LPMark View Post

R Siminoff states in the "Luthiers Handbook" that for acoustic instruments with a FIXED bridge that "little or no power comes from the lateral vibration".
Lateral vibration causes the greatest string excursion and is the limiting factor of how low the action can be and appears to be affected by resonance of the entire system.
I think you are misunderstanding Roger S; something that is not hard to do.

Most of the power that the string transfers to the top comes from the string's transverse motion--motion perpendicular to the string. That motion can be anywhere in the 360º around the string, and is not just in one plane at a time--the string gyrates around its resting line as well as displacing side to side. If you look only at the motion that is parallel to the top, which I'd assume is what Roger is calling "lateral," it transfers little movement or power to the top. However, that lateral transverse movement, because it is parallel to the fretboard, has nothing to do with limiting action height. What limits action height is the transverse movement perpendicular to the top and fretboard, and that is exactly the movement that provides most of the acoustic power. So there is no free lunch available here. You could make the top move less--until eventually it becomes like a solid-body electric guitar--and by losing the top's resonant motion reduce string excursion and get the action a very little bit lower; but this would come at the cost of losing acoustic power and tone.
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Last edited by Howard Klepper; 04-14-2017 at 12:20 PM.
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Old 04-14-2017, 01:01 PM
Alan Carruth Alan Carruth is offline
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Thanks Howard.
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Old 04-15-2017, 05:24 PM
LPMark LPMark is offline
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Simonoff is pretty clear on that point where he demonstrates an experiment with a test jig that inhibits bridge movement in the direction laterally to the string axis [up and down on the plate] and then a rocking motion [rotation around the axis of the saddle] and measures acoustic output and shows a considerable decrease when rocking motion is inhibited over up and down motion of the bridge. It is true that the lateral vibration is not in one plane but will rotate through 360deg as the note decays.

So the conclusion is that the lateral vibration of the string also causes a corresponding change in tension along the strings length and this is the vibrational energy that is transferred to the soundboard with "Fixed Bridge" instruments but not movable bridges because they cant impart rotational force to the top plate.


So I'm wonder if anyone has considered this in design, has found a practical application or disputes this assumption.
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Old 04-16-2017, 01:39 PM
Alan Carruth Alan Carruth is offline
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Although I have not replicated Siminoff's experiment exactly as he has done it, I've done the same thing in different ways, and get very different results. I've spent 'way too much time on this, and seem destined to spend some more: strings are the simplest parts of the guitar, but they're not simple.

Some years back, when there was a discussion of this on another forum on line, I looked up the section on strings in Fletcher and Rossing's "The Physics of Musical Instruments", which is a standard text in the field. They gave equations for calculating the transverse force of the string on the saddle top, and also the tension change. If you solve these they indicate that, for the most part, the transverse force is the larger of the two. Since I'm out of practice with the math, I decided I'd check it out with some experiments. Although I saw some things that I didn't expect, which necessitated spending a lot more time than I'd expected, what I saw pretty much confirmed the math in that respect.

Basically, if the string is vibrating 'up and down' relative to the plane of the soundboard, it is pulling the bridge up and down. In the process, the tension also changes: whenever the string is all the way 'up' or 'down', the tension is higher. On the average, the vertical 'transverse' force will be on the order of seven times as great as the 'longitudinal' tension change force, although it varies a lot depending on the string.


As has been pointed out, it's hard to push a bridge sideways by much. It can rock a bit as the top flexes, of course, but not much.

The bridge can also rock forward and backward as the string tension changes. If you measure how much motion you get for a given force in this direction at different frequencies it's not much. Of course, the bridge is at the fulcrum of the see-saw, so to speak, and small motion there can give more motion further out. Still, we do build guitar tops to resist that sort of deformation, so, although it amounts to more overall motion in the top, it's not all that much greater than the crosswise rocking for a given force. Keep in mind here that when the bridge rocks forward, it pushes the top down between the bridge and the soundhole, and pull it up in back toward the tailblock. The two motions cancel each other out to some extent, which would reduce the sound produced.

Pushing the bridge vertically, causing the top to move like a loudspeaker cone, is pretty easy by comparison. This also tends to move the whole lower bout of the top in the same direction at once, which can move a fair amount of air and produce some sound.

Thus:
1) the vertical transverse force is greater than the tension change, and
2) it pushes on the top in a way that it easier to move,
3) that is more efficient at turning that motion into sound.

I did two experiments using an un-modified guitar to check this out. In one I used an electromagnetic system to drive a string with a 'pure' sine wave signal. The other used a mechanical plucker to get the string moving in only one direction, with a known force at a given location (so the string produced a mix of frequencies). In both cases the output of the guitar, as measured with a dB meter out in front, was much greater when the string moved 'vertically' with respect to the soundboard than when it moved 'horizontally'; parallel to it. The 'vertical' string motion drives the 'loudspeaker' top movement via the transverse string motion, while the 'horizontal' string motion can only cause the bridge to rock forward and back or side to side.

Keep in mind, too , that since the tension change happens twice for every full cycle of the string vibration, it should sound an octave higher. Flat top guitars with the strings tied or pinned to the bridge can cause it to rock forward and back with the tension change. Archtop guitars, where the string tension is taken up by a tailpiece, and the bridge is not glued down, can only work by the transverse force on the bridge. If flat tops were primarily driven by a twice per cycle tension change, why would they not sound an octave higher the archtops?

I could go on, but I've belabored this subject for a long time already on these fora. I presented a talk at an ASIA meeting some years back, which was reprinted in 'Guitarmaker', and is also available on my web site as a .pdf file entitled 'String Theory' (I could not resist). At some point, as I find out more, I hope to refine that, but, as I say, there's more going on than you might think.
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