Paper: A Data-Driven Approach to Violin Making


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16 hours ago, Marty Kasprzyk said:

I think it is a mistake to ignore the cross grain elastic elastic modulus or its cross grain speed of sound because it does have a large effect. 

Cremer's (1) equation 11.24 seen below used a simple flat rectangular plate to model the mode frequencies of a violin top. If the width Lx of the plate for example is one half the length Ly then, because they are squared, the width direction contribution is four times greater than the long direction.   But the wood's cross grain speed of sound Cx is typically only one fourth of the longitudinal speed of sound Cy so both directions contribute the same amount to the calculated plate frequency.

The speed of sound C equals the square root of the elastic modulus/density ratio.  So the 4 to 1 ratio of their speeds of sound produces a 16 to 1 ratio of their elastic modulus stiffness.  This  anisotropy ratio is in the range of spruce wood.  Cremer's equation shows that it is important to have a high cross grain stiffness because this allows the plate to be made thinner and therefore lighter while still producing the same mode frequency.  This in turn increases the loudness of the violin.

Makers are careful to choose top plate wood which has its growth rings perpendicular to the cross arch surface in order to maximize its cross grain stiffness and speed of sound.  An off-angle reduces the stiffness and therefore the plate has to be made thicker (thus heavier) which reduces the violin's sound output.

We also know the tops of many famous old violins were thinned sometime long after they were made.  Some contemporary makers have also regraduated their own violin's plates several years after they were built.  I assume this was done because they might have eventually sounded too bright or even harsh.  Thinning reduces the frequencies of the resonance peaks across the entire violin's spectrum and Claudia Fritz has shown that it only takes about 1.5 to 5 percent frequency change to be perceived.

Martin Schleske (2) has shown how various kinds of varnish increase the speed of sound in the cross grain direction quite a bit over a nine year period.  I assume this is because the varnish is getting harder and stiffer which may explain why plates were sometimes regraduated.

The attached graph (3) shows how the plate should be made thicker or thinner depending upon its cross grain speed of sound using a wood with a longitudinal speed of sound of 5200m/sec. A nominal 3mm thickness at a 1300m/sec cross grain speed of sound(4 to 1 ratio) is shown by the red lines.  It doesn't take much of an increase in the cross grain speed of sound to require some thinning to maintain the same mode frequency of  1351 radians/sec or 215Hz.

1.  Lothar Cremer, "The Physics of the Violin", The MIT Press, 1984, p291

2. Martin Schleske, On the Acoustical Properties of Violin Varnish, CASJ Vol 3, No 6, November 1998

3. me, right now

 

Cremer.jpg

Screen Shot 2021-02-24 at 2.01.43 PM.png

Dear Marty, I am impressed with your analyses! Thanks for sharing them.

I have recently learnt that OSB-strand plates are ortothropic, somwaht like plain wood. The «slow direction» gave the most dominant critical frequency. This was related to a test tube we have at work and we measured the sound insulation from outside to the inside. The sound insulation curve show a dip at the critical frequency. If we had been driving the plate mechanically we would probably have seen a top in the radiated spectrum at the frequency. 
Maybe a similar effect happens in violins? 

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On 2/24/2021 at 12:46 PM, Don Noon said:

The Strad plot illustrates what I have been harping about forever. 

'harping' in a violin making discussion forum is probably not a good idea. :D

On 2/24/2021 at 12:46 PM, Don Noon said:

Only when you get above that, the huge difference is obvious.  And it agrees well with the few Strads I have been able to measure:  abnormally strong response between 1 and 2 kHz, whereas modern ones almost never hit their "bridge hill" stride until much higher frequencies.

That's an interesting observation. I was trying to find material on the bridge hill and the papers i could dig up from the net describe it differently though 

Many excellent violins show a broad peak of response in the vicinity of 2.5 kHz, a feature which has been called the “bridge hill” (On the “Bridge Hill” of the Violin J. Woodhouse) 2005

http://www2.eng.cam.ac.uk/~jw12/JW PDFs/BridgeHill.pdf

So do you think the low bridge hill resonance is unique to Strad?

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37 minutes ago, Andreas Preuss said:

'harping' in a violin making discussion forum is probably not a good idea. :D

That's an interesting observation. I was trying to find material on the bridge hill and the papers i could dig up from the net describe it differently though 

Many excellent violins show a broad peak of response in the vicinity of 2.5 kHz, a feature which has been called the “bridge hill” (On the “Bridge Hill” of the Violin J. Woodhouse) 2005

http://www2.eng.cam.ac.uk/~jw12/JW PDFs/BridgeHill.pdf

So do you think the low bridge hill resonance is unique to Strad?

The Woodhouse paper you cited has a reference which I think shows some interesting violin experiments rather than  mathematical predictions.

[6] E. V. Jansson, B. K. Niewczyk: On the acoustics of the vi- olin: bridge or body hill. J. Catgut Acoust. Soc. Series 2 3 (1999) 23–27.

 

One of Jansson's experiments shows the effect of adding stiffening strips across the f hole island.  The bridge hill frequency changes dramatically.

 

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On 2/28/2021 at 12:29 AM, Marty Kasprzyk said:

The Woodhouse paper you cited has a reference which I think shows some interesting violin experiments rather than  mathematical predictions.

[6] E. V. Jansson, B. K. Niewczyk: On the acoustics of the vi- olin: bridge or body hill. J. Catgut Acoust. Soc. Series 2 3 (1999) 23–27.

 

One of Jansson's experiments shows the effect of adding stiffening strips across the f hole island.  The bridge hill frequency changes dramatically.

 

Thanks for forwarding this. I made a printout and still have to chew on the contents with my limited knowledge of physics.

If it is possible to shift the BH resonance frequency (or resonances?) by altering the zone around the bridge it should be also possible to change it by the down pressure and location of the bridge, or not? 

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32 minutes ago, Andreas Preuss said:

it should be also possible to change it by the down pressure and location of the bridge, or not? 

First-order physics:  not.  Structure vibration frequencies are mostly independent of static forces.

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54 minutes ago, Don Noon said:

First-order physics:  not.  Structure vibration frequencies are mostly independent of static forces.

Then this means that the way the thicknesses around the bridge are designed have a paramount importance on the overall sound of a violin?

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1 hour ago, Andreas Preuss said:

Then this means that the way the thicknesses around the bridge are designed have a paramount importance on the overall sound of a violin?

That would be an implication of the paper... although it doesn't rule out plenty of other things being of paramount importance as well.

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On 2/27/2021 at 3:44 PM, Andreas Preuss said:

So do you think the low bridge hill resonance is unique to Strad?

It is probably a feature of a reverse graduated violin, or one with a thin central top plate region. It is not likely to be unique to Strads, but to violins in general with that trait. I guess it differs from violins with a thick central region which many modern violins did have up to quite recently, according to Joe Curtin in a recent talk.

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On 3/1/2021 at 11:57 AM, Anders Buen said:

It is probably a feature of a reverse graduated violin, or one with a thin central top plate region. It is not likely to be unique to Strads, but to violins in general with that trait. I guess it differs from violins with a thick central region which many modern violins did have up to quite recently, according to Joe Curtin in a recent talk.

That's what I think too.  Thin sounds good but is weak.  

There is a limit of how thin you can go in the quest for better performance.  I remember a USA sailboat doing really well in a 12 meter American Cup race until it broke in half.

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