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More explanation for the "why" of violin arch shapes


Roger Hill
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“We found a mathematical argument that explains how and why this robust effect exists with any shape within this class, so that the details of the shape are unimportant, and the only fact that matters is that there is a reversal of curvature along the saw.”

Location of inflection is apparently unimportant, though its existence is everything.  Enjoy

https://www.seas.harvard.edu/news/2022/04/physics-singing-saw

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12 hours ago, Roger Hill said:

“We found a mathematical argument that explains how and why this robust effect exists with any shape within this class, so that the details of the shape are unimportant, and the only fact that matters is that there is a reversal of curvature along the saw.”

Location of inflection is apparently unimportant, though its existence is everything.  Enjoy

https://www.seas.harvard.edu/news/2022/04/physics-singing-saw

That's quite interesting.

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10 hours ago, Dennis J said:

If this effect holds true with violin arching it might be that confining the sweet spot to a well defined area between convex and concave, not flat, would be an acoustic enhancement.

I am thinking that the "sweet spot" is a trapped (isolated) mode between the curves, and only would be energized by direct excitation.  The musical saw requires bowing at the exact inflection point... bow elsewhere, and you get nothing.  So the recurve on a violin might be more of a "dead spot", since the bridge energy is entered elsewhere.

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52 minutes ago, Don Noon said:

I am thinking that the "sweet spot" is a trapped (isolated) mode between the curves, and only would be energized by direct excitation.  The musical saw requires bowing at the exact inflection point... bow elsewhere, and you get nothing.  So the recurve on a violin might be more of a "dead spot", since the bridge energy is entered elsewhere.

I agree.  I put the inflection point line right over the sound post position for my bent saw shape back on the violin I'm making.  The original idea was to get rid rinky-dink shoulder rests but there might be some acoustical advantages too.

39 back .JPG

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As someone who made a good living analyzing the vibration of many different structures, this article made my head hurt.

The primary mechanism of vibration for thin structures is deflection perpendicular to its surface, curved or flat.

The sharply curved or "J" shaped saw has substantial restraints at both ends which restricts the deflection of the lower modes of vibration. Draw arrows anywhere perpendicular to the surface and you will see significant components of that deflection which resolve transversely along the sheet to a restrained boundary condition. 

The gentle recurve which is little more than a flat sheet with a small offset at the ends has no such restraints on deflection perpendicular to the surface.

There is no secret sweet spot being discovered at Harvard. If you want a membrane to vibrate strongly, choose a shape whose perpendicular deflections do not resolve into transverse constraints.

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3 hours ago, ctanzio said:

As someone who made a good living analyzing the vibration of many different structures, this article made my head hurt.

The article for me was fairly opaque, probably as a failed attempt to dumb down the research for public consumption.  The referenced actual paper made my head explode.

However, just skimming the paper in a non-head-exploding way, and assuming the analysis is correct, there is a statement about a "localized mode" (what I called trapped or isolated mode) with a high Q (low damping) that can be energized for a sustained vibration.  So my previous post still holds.

The "sweet spot" is no secret, as musical saws have been played for at least a century.  The discovery is the complex math to explain it.  Violins are infinitely more complicated.

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While this is interesting info in its own right, I'm doubting that it relates to violins at all.

The scenarios are very different.  Violin we can observe substantially works via driven standing waves.   Bowed saw combines directly stimulated initial pitched resonance with radiating surface in one.

No real relationship.

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1 hour ago, David Beard said:

While this is interesting info in its own right, I'm doubting that it relates to violins at all.

The scenarios are very different.  Violin we can observe substantially works via driven standing waves.   Bowed saw combines directly stimulated initial pitched resonance with radiating surface in one.

No real relationship.

That's what my post was eluding to, really it's as simple as apples and oranges, and how there is no comparison.

I would agree with Don, that as far as we are concerned the recurve and it's relationship to what matters is that it is "the beginning of the end" and very much establishes the "event horizon" to which once frequency waves pass that region there will be no coming back to interact with "the other side" as if "Alice were the wave and Bob was the plate and "other" waves interacting inside that boundary.

And so then the question, "can my carving and small mm' location changes of the bottom of my valley of my recurve and it's relation to the rib structure and linings below that, as well as "what happening on the underside of my recurve" effect my over all sound"  the answer is yes

That being said, this recurve area is important related to"other things" such as it's influence on oscillation of the entire plate in various modes and well lots of other stuff that I'm sure we could argue over for days. but in general this saw bowing stuff hasn't much to do with violins except maybe the bow.

 

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9 hours ago, Don Noon said:

I am thinking that the "sweet spot" is a trapped (isolated) mode between the curves, and only would be energized by direct excitation.  The musical saw requires bowing at the exact inflection point... bow elsewhere, and you get nothing.  So the recurve on a violin might be more of a "dead spot", since the bridge energy is entered elsewhere.

Yes, I do realise that. I have wondered whether well defined arching profiles with a clear inflection point, achieved with precise arching guides, is desirable or not.

I get the impression that a lot of makers relying on arching by eye are creating profiles where the upper convex and lower concave scoop is separated by a flat section.

So the possible consequences are it doesn't make any difference or it is positive or negative acoustically.

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1 hour ago, Dennis J said:

So the possible consequences are it doesn't make any difference or it is positive or negative acoustically.

Possible consequences: 1) no difference  2) there is a difference... which some people will prefer, and others won't, and the results most likely would change depending on who is playing and what hall it is played in.

oh... and that latter part would also apply to 1) as well.

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I just thought about the frequency of the "sweet" (or dead) spot of the inflection of a violin top.  By my rough calculations, it would be in excess of 20kHz... so I'd throw this idea on the trash heap, at least as it pertains to violin acoustics.

I still think that the location of the inflection is important... but not for this reason.

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As mentioned the inflection surface/lines go through the sound holes, just about through the middle as I locate it.

I just like the idea of keeping it well defined and narrow assuming that is the best option. I think inevitably there really is a big difference using templates to achieve that and freehand arching.

 

 

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