Damping of the violin bodies

[Anders Buen]

In my diploma work, equivalent to a Master of Science thesis, I studied violins using an advanced TV-holography system. I measured the resonances, the amplitudes and the damping from a set of five instruments including av Gaetano II Guadagnini. The fixture of the violins had to be somwhat stable due to the sensitive optic interfermometric system, so the fiddles stood on a piece of foam rubber and rested against a rubberized lab claw, of those used for holding test tubes in chemistry.

I just found a file with the regression data from that thesis compared to Bissingers measurements on his 17 instruments, which have been reated by a pro player into good and bad. I am not sure if any of the fine old violins is included here or not. We may figure out that.

Bissingers fixture is the fiddle upside down and, I believe, without damping of the strings. I damped the strings to avoid string resonances to influence the measurements. 

My damping values are quite a bit higher than Bissingers, probably related to the lossy fixture of mine, as well as the damped strings. I also show Craiks simple formula for loss factors in empty double walls or even massive ones in similar forms. Eta = 0,005 (internal loss) + 0,4/(f^0,5). This is an Statistical Energy Analysis formula. You see the trends follow his formula pretty much. 

In reality the damping jump up and down, mainly related to the dominance of crossgrain or along grain bending, as well as different natures of modes. Some are active in the interior air, some wings move etc. What we see here is trends.

I share this before the curves "sink into subconsciousness" on an old computer I have. 

In general those who do modal analysis and extract model parameters like damping agree that damping is not different, in general, between old and new intruments. Schleske, Stoppani and we will see also the pre and post WW2 researchers came to that concusion, I think. Having said that, damping does influence the frequency response and loudness of structures, so it may play an important role anyway. Holding the instrument for playing, influences the damping of the violin body quite much, at least in the low and mid frequency range. My opinion is that it dominates in this region, and that efforts to change the losses are not effective there. But may be for higher frequencies.   

 

 

[Don Noon]

33 minutes ago, Anders Buen said:

In general those who do modal analysis and extract model parameters like damping agree that damping is not different, in general, between old and new intruments. Schleske, Stoppani and we will see also the pre and post WW2 researchers came to that concusion, I think. Having said that, damping does influence the frequency response and loudness of structures, so it may play an important role anyway. Holding the instrument for playing, influences the damping of the violin body quite much, at least in the low and mid frequency range. My opinion is that it dominates in this region, and that efforts to change the losses are not effective there. But may be for higher frequencies.   

I do not have objective data for proof, but it is quite clear to me (and some other makers) that torrefied wood gives a distinctively brighter sound.  This hold true even when the torrefied wood is not any different in density and stiffness compared to normal wood.

That leaves damping as the most likely suspect.  And just from logic, less energy absorbed by the structure should equal more amplitude in vibrations and more sound output, particularly in the high frequencies where the modes all run together.  I have tried, as others have, to measure damping in the completed violin... but it's not easy, and the measurements jump all over the place, with questionable results in the end.

[Anders Buen]

1 hour ago, Don Noon said:

I do not have objective data for proof, but it is quite clear to me (and some other makers) that torrefied wood gives a distinctively brighter sound.  This hold true even when the torrefied wood is not any different in density and stiffness compared to normal wood.

That leaves damping as the most likely suspect.  And just from logic, less energy absorbed by the structure should equal more amplitude in vibrations and more sound output, particularly in the high frequencies where the modes all run together.  I have tried, as others have, to measure damping in the completed violin... but it's not easy, and the measurements jump all over the place, with questionable results in the end.

I guess this makes sense. For flat plates for walls etc we see the damping effect mainly at or above the coincidence frequency. However, measuring the damping of the violin body in a vibration insulated rig, or by holding it, there is a fairly dramatic change of the response. The tops becomes weaker and the vallies shallower. So the damping does work on the modes below coincidence as well. Much building acoustics theory is "average response", statistical energy analysis, disregarding the modes, or assuming a high modal density. 

I look through, and brush up the graphs, in a file with damping data from Saunders, Lottermoser, the first Modal analysis by Kenneth Marshall, Bissinger and some data I have collected myself, including a couple from two Ole Bull reated del Gesus. 

We do room acoustics and the program we use also was used for a PhD work on violins. One possible way to measure damping is by using room acoustic impulse response processing. However, one need a close mic or an acclerometer to minimize the effect from room reverb (usually larger). A very dead room may help. The strings also needs to be damped, including afterlengths and possible ringing strings in the pegbox. I think it can be done with a smartphone with a room acoustics program too. Maybe not available for free. Maybe REW for PC can do it? It is a freeware for studio measurments.

There is a relation between structural reverberation time and loss factors. T60 = 2,2Q/f0 = 2,2/(f0*eta).

There are several parameters describing damping, which makes it a bit confusing. One of the problems of sharing the info. In room acoustics the "running reverb" is what we hear while listening to music or speech. It is given by the Early Decay time EDT and is mesured in the early part of the decay time, and then the curve is extrapolated down to -60 dB. 

I guess that the wooden decay and buildup is affected by the damping. I guess a more damped structure reaches max a bit faster, although at a somwehat weaker maks than a less damped structure. Maybe decay times makes most sense?

In one of the tables (on Marshalls data) I have a column called decay time it is 1/6th the T60 given above and may be similar to a "heard reverb". 5% changes to reverberation times are usually just about detectable. Maybe that works for such shorter decays as the violin body? Usually we hear the ringing strings which have reverbtimes far beyond most living rooms or workshops.

Edited August 31, 2021 by Anders Buen
Corrected spelling errors

[Don Noon]

11 minutes ago, Anders Buen said:

I guess that the wooden decay and buildup is affected by the damping. I guess a more damped structure reaches max a bit faster, although at a somwehat weaker maks than a less damped structure. Maybe decay times makes most sense?

I tried measuring damping with a sine pulse and voice coil bridge driver.  Buildup and decay times seemed similar for the buildup and the decay, as makes sense.  However, the times varied widely depending on frequency, and I didn't feel like making a zillion measurements and doing the statistical analysis on them... and doing that for a bunch of different instruments for comparisons.

[Anders Buen]

19 minutes ago, Don Noon said:

I tried measuring damping with a sine pulse and voice coil bridge driver.  Buildup and decay times seemed similar for the buildup and the decay, as makes sense.  However, the times varied widely depending on frequency, and I didn't feel like making a zillion measurements and doing the statistical analysis on them... and doing that for a bunch of different instruments for comparisons.

I guess you have a good understanding of what happens after doing own experiments on this, which is a good thing. I think your method is quite similar to what Saunders with helpers did, except for their use of a high speed camera and film. I wonder if Norman Pickering did extract that kind of information, in addition to the spectra. Or helpers. 

The needle is a bit mass loading there. But I do not know how much. 

[ctanzio]

Damping estimates from sound decay measurements pose a challenge to extract useful material information because of the variety of effects that cause the sound to decay: internal wood damping, non-projecting resonators like the tail piece and finger board, and sound radiation into the air.

If one could measure the energy loss just from sound radiation, one would probably find geometric conditions, like plate mass and arching, dominate the effect. But it is not realistically possible to separate these different effects from decaying sound recordings because there is no way to physically remove internal damping and non-projecting resonant effects from radiation loss using this method.

One thing you can do to estimate internal wood damping, and thus some "quality" measurement of the wood itself, is to do a frequency sweep about a mode resonate frequency, and compute something called the half-power bandwidth ratio. Since the violin body is being driven at a steady state sound output, the radiation effects are canceled, and the damping response becomes that of (mostly) internal wood damping.

If you do an Audacity spectral response plot of dB versus frequency, find a resonance peak. Find its dB level.

Now subtract 6 from it to get the half power level.

Follow the curve on either side of the peak until you reach this half power level and note the frequencies: one higher than the resonate peak and the other lower.

Subtract the lower from the higher and divide by the frequency of the resonate peak. This is a guestimate of the internal damping at the resonate frequency.

You can repeat this for as many resonate peaks as is possible to get an idea of how material damping varies with frequency.

This works for "small" values of damping. A more accurate formula is:

damping = {0.5 - [0.25 - 0.0625 x ((f2-f1)/fr)^2) x ((f2+f1)/fr)^2)]^0.5 }^0.5

f1 = lower half power frequency

f2 = higher half power frequency

fr = resonate frequency

The method would also be applicable to a wood billet, but the challenge would be in setting the dimensions to get a range of resonate frequencies in the same range as a violin.

[Don Noon]

54 minutes ago, ctanzio said:

If you do an Audacity spectral response plot of dB versus frequency, find a resonance peak. Find its dB level.

Now subtract 6 from it to get the half power level.

Isn't the half power level -3 dB?  

This method might work if you have a clean, clear peak with no other resonances too close, so clean signature modes might work.  Higher than that, things get very messy, with lots of modes close together, so I doubt you'd really know what you're looking at.  And it's those higher frequencies that I'm most interested in.

[Anders Buen]

4 hours ago, Don Noon said:

Isn't the half power level -3 dB?  

This method might work if you have a clean, clear peak with no other resonances too close, so clean signature modes might work.  Higher than that, things get very messy, with lots of modes close together, so I doubt you'd really know what you're looking at.  And it's those higher frequencies that I'm most interested in.

I think so if the data shown is 10log(p^2) = 20log(p)

I extracted the damping of the violins and in violin plates up to about 1,2 kHz ish with the Holography system. Some modes may work for extraction, some don't in the highs. 

[Anders Buen]

I enclose plots of the quality factor measured from impulse responses of a fiddle in Curtins rig on rubberbands, and held for playing. I recorded the responses with an accelerometer near the bridge or at it. 

The second graph also show the Q values from a 20 cm distant microphone. And we see that the apparent measured iverse damping (Q = 1/eta) becomes higher due to the much narrower resonances in my living room lab. 

Finally I show a graph of the same examples held and in rig, comared to regression data from my TV-holography study, as well as two of Bissingers regression curves. They fit better with the rig mounted violin as expected. The TV Holography study show more damping than the rig mounted situation, also as expected.

The higher Q's in the highest frequencies may come from ringing string bits in the pegbox. There was foam rubber fatened between the strings and the afternlengths, probably adding some damping to the body too.

Some years a go Fritz et al did experiments with changing resonances of violins, like the damping, frequencies and amplitudes. In the "meat text" there they do not seem to be awere that the damping of a violin is much influenced by holding it, as well as from variation in relative humidity. They came to results indicating that a slightly higher damping was preferred. That can be caused by the experience with the violins being more damped than we measure them. A pretty obvious explanation.

Jansson did measure this effect many years ago and show the resonances. In his work it seeme as the highs got a boost and the lows became more rounded and weaker.    

[Anders Buen]

An other comment on measuring damping in structures using reverberation time algoritms. I have recently learnt that the filters involved in measurement equipment for such measurements do have a final reverberation time itself. That is the 1/3rd octave band or 1/1 octave band filters have a lower limit for how low reverberation times they can handle.

This lower limit becomes lower for the wider bands than the narrower bands. So next time I will do the tests in octave bands. 

[Anders Buen]

5 hours ago, ctanzio said:

This works for "small" values of damping. A more accurate formula is:

damping = {0.5 - [0.25 - 0.0625 x ((f2-f1)/fr)^2) x ((f2+f1)/fr)^2)]^0.5 }^0.5

f1 = lower half power frequency

f2 = higher half power frequency

fr = resonate frequency

I have never seen this before. Do you have a refrence for it?

[Anders Buen]

I enclose a set of graphs from the same insturment suing three different techiques for extracting the data:

1. Mode fitting from a modal analysis (MA)

2. Structural RT from an impulse response picking up the signal with an accelerometer

3. An IPhone with StudioSixDigitals reverberation time app one test with undamped strings and one with damped strings

I believe I have held the IPhone close to the instrument. I do also have an opportunity to connect an accelerometer to an IPhone or similar device and use the same program. I am not sure what I did 9 years ago. However, there is probably an older thread on this, becaus I found the file in a map for a Maestronet discussion.

Structural reverberation time can be compared to Q by: RT = 2,2Q/f0

Q=1/eta

EDT is the reverberation time asessed from the first -5 dB to -25 dB or so (I do not remember the exact numbers), the first and most audible part of the decy.

I guess reverb is the best descriptor of damping, as we fairly easyly hear differences larger than about 5% in RT. We do also hear well if something rings longer than the rest, like the open strings.

Edited September 2, 2021 by Anders Buen
Corrections and added some more info.

[ctanzio]

4 hours ago, Don Noon said:

Isn't the half power level -3 dB?  

My understanding is the Audacity plot is the dB level of the amplitude of the sound wave. Since power is proportional to the amplitude squared, a -6dB drop in amplitude gives a -3dB drop in power. Let me know if you want me to bore you with the math. It only takes a few steps to derive.

If all you want is some relative measure of damping, not a theoretical rigorous measure that one can plug into an equation, the actual dB drop used to get the width of the resonance peak is somewhat arbitrary.

[Marty Kasprzyk]

Assuming a good way of measuring violin body damping is found--does anybody have an opinion on what level of damping is best?  

[ctanzio]

1 hour ago, Anders Buen said:

I have never seen this before. Do you have a refrence for it?

The simply half power bandwidth formula, r = (f2-f1)/(2fr),  is derived by assuming peak power occurs at the resonance frequency. But in reality, it occurs at the UNDAMPED resonance frequency, something that cannot be directly measured from a damped system.

For systems that are lightly damped, the damped and undamped resonance frequencies are close enough to use the simple formula when r < 0.05. For larger values of damping, there is an entire field of research dedicated to deriving various formulas to give a better measure of the damping. I believe the formula I quoted was for a mode shape similar to a vibrating cantilever bar.

Do a search on the terms "damping ratio", "frequency response function" and "dynamic data" and be prepared for a lot of math and experimental data. There might be a formula that is more relevant to violin modes.

[ctanzio]

16 minutes ago, Marty Kasprzyk said:

Assuming a good way of measuring violin body damping is found--does anybody have an opinion on what level of damping is best?  

This is a tough question. It depends on what you want to achieve. If you just want loud and fast bow response, the answer is as small as possible. But the violin might start sounding more like a ringing bell than a violin. Don Noon with his experience with torrified wood might be in a better position to comment on low damping and violin tone.

[Don Noon]

2 hours ago, ctanzio said:

My understanding is the Audacity plot is the dB level of the amplitude of the sound wave.

I searched around in Audacity, and couldn't find anything that explicity says what the dB of the spectrum plot is.  I had just assumed dB's were all the same.

I will eventually check amplitude decay vs. the -3 and -6 dB of the spectral plot and see how the damping calculations compare.  Presumably I should use the highest resolution plotting, to avoid as much smoothing as possible.

1 hour ago, Marty Kasprzyk said:

Assuming a good way of measuring violin body damping is found--does anybody have an opinion on what level of damping is best?  

That would have to wait until a good way of measuring violin body damping is found, and then see what damping corresponds to the "best" sound... whatever that is.

But since you asked for an opinion... more than zero but less than most... if you like bright and lively (some don't).  I base this on torrefied wood results, where wood damping is measurably lower than untorrefied wood, and yet adding varnish (which adds damping, but modifies stiffness as well) seems to give a more desirable tone and playability.

[jezzupe]

5 hours ago, Marty Kasprzyk said:

Assuming a good way of measuring violin body damping is found--does anybody have an opinion on what level of damping is best?  

Well just the right amount Marty, duh

Out of all the properties damping will be the one that is not stable and changes, and or will be directly related to the emc of the wood and the weather or room conditions. So I certainly hope any of these tests have a standardized temp and humidity reading as well as multiple accurate pinless readings of the material itself prior to any of this testing so that things are universal and "everyone's" test's are starting at the same place.

I do think Marty's question is the most important one, because it is the one that has some level of control , or damping can be "built in" with coatings,and other small things, both interior and exterior, so there is some control but I don't think anything concrete.

I do feel damping is perhaps the most important property for getting that "Stradavaius" ropey nasal tone, and that Torrified material will help make a very loud clear instrument but that the material may be "too hot" and be missing some damping.

When I get back to it I plan on experimenting with "half torrified" plates, meaning I will be experimenting with splits , where one half is torrified, and the other is not, and then build a few variations alternating treble/bass side. I have a feeling that it might produce interesting results 

I want my bass to be torrified, but not the treble, so I think it will be interesting to see if there is a difference

[Anders Buen]

9 hours ago, ctanzio said:

The simply half power bandwidth formula, r = (f2-f1)/(2fr),  is derived by assuming peak power occurs at the resonance frequency. But in reality, it occurs at the UNDAMPED resonance frequency, something that cannot be directly measured from a damped system.

For systems that are lightly damped, the damped and undamped resonance frequencies are close enough to use the simple formula when r < 0.05. For larger values of damping, there is an entire field of research dedicated to deriving various formulas to give a better measure of the damping. I believe the formula I quoted was for a mode shape similar to a vibrating cantilever bar.

Do a search on the terms "damping ratio", "frequency response function" and "dynamic data" and be prepared for a lot of math and experimental data. There might be a formula that is more relevant to violin modes.

In my diploma work from 1993/94 I found this formula addressing this (from Rao Singiresu S Mechanical vibrations, Addison Wesley Publ Comp, 1990, 718p):

r = f/f0 

r1,2 = (1-2*(eta/2)^2 +/- eta(1+(eta/2)^2)^0,5)^0,5

When eta is small this expression simplifies to:

r1,2 = 1 +/- 2* (eta/2)^0,5

The simple version gives this expression for the determination of the damping factor:

Eta = (f2-f1)/f0

Trying with different numbers for eta will give an idea when it makes sense to use the complex or the simple formula. I do think that anything you measure in a violin with damping factors varying from 0,1-0,03 or so, the simple formula is more than good enough.

The major issue with measurements of damping is the losses due to fixture and imperfect placing of the resting lines. However, it does not matter what damping is measured in the violin because holding the violin for playing will dominate the damping anyway. 

[Salve Håkedal]

Most of this is way above my head. But regarding torrefied wood giving brighter sound: Does torrefying alter the ratio of stiffness between longitudinal and radial direction in the wood (trunk)?

[Andreas Preuss]

Kind of interesting topic, but I am wondering what is the whole picture of damping effects.

In a general sense ‘damping’ is associated with a negative effect, but when it comes to violin sound, things are for ‘sound aesthetics’ not so simple.

Good violinists ravish about violins which have seemingly infinite possibilities to create different sound colors. So I would rather ask if damping can be controlled by the player as a mean of expression. Presumably in physics this means rather to look on damping related to bowing energy input and not on relations to frequencies. 

[Anders Buen]

12 minutes ago, Andreas Preuss said:

Good violinists ravish about violins which have seemingly infinite possibilities to create different sound colors. So I would rather ask if damping can be controlled by the player as a mean of expression. Presumably in physics this means rather to look on damping related to bowing energy input and not on relations to frequencies. 

Sometimes cellists dampen the body of the instruments with their legs to mitigate the wolf. 

[Don Noon]

7 hours ago, Salve Håkedal said:

Does torrefying alter the ratio of stiffness between longitudinal and radial direction in the wood (trunk)?

Unfortunately I don't have good before/after data for crossgrain stiffness, as I can only measure the crossgrain with cut samples... which I am only willing to do from offcuts after I cut out the plate.

However, I don't see anything earthshakingly abnormal in the torrefied wood measurements re: stiffness ratios.

[Don Noon]

3 hours ago, Andreas Preuss said:

Good violinists ravish about violins which have seemingly infinite possibilities to create different sound colors. So I would rather ask if damping can be controlled by the player as a mean of expression. Presumably in physics this means rather to look on damping related to bowing energy input and not on relations to frequencies. 

To me, "different sound colors" implies an instrument with a broad response curve with minimal dropouts or ragged peaks, so that the player can access a maximum variety of frequencies.  I don't see it as something that can be player-controlled, other than the usual bow pressure and distance from the bridge, which changes the string input to the body but does not affect the body acoustics itself.  And there's the limited possibility of clamping down on a chinrest to dampen a wolf.

[Marty Kasprzyk]

3 hours ago, Andreas Preuss said:

Kind of interesting topic, but I am wondering what is the whole picture of damping effects.

In a general sense ‘damping’ is associated with a negative effect, but when it comes to violin sound, things are for ‘sound aesthetics’ not so simple.

Good violinists ravish about violins which have seemingly infinite possibilities to create different sound colors. So I would rather ask if damping can be controlled by the player as a mean of expression. Presumably in physics this means rather to look on damping related to bowing energy input and not on relations to frequencies. 

 

17 hours ago, Anders Buen said:

I enclose plots of the quality factor measured from impulse responses of a fiddle in Curtins rig on rubberbands, and held for playing. I recorded the responses with an accelerometer near the bridge or at it. 

The second graph also show the Q values from a 20 cm distant microphone. And we see that the apparent measured iverse damping (Q = 1/eta) becomes higher due to the much narrower resonances in my living room lab. 

Finally I show a graph of the same examples held and in rig, comared to regression data from my TV-holography study, as well as two of Bissingers regression curves. They fit better with the rig mounted violin as expected. The TV Holography study show more damping than the rig mounted situation, also as expected.

The higher Q's in the highest frequencies may come from ringing string bits in the pegbox. There was foam rubber fatened between the strings and the afternlengths, probably adding some damping to the body too.

Some years a go Fritz et al did experiments with changing resonances of violins, like the damping, frequencies and amplitudes. In the "meat text" there they do not seem to be awere that the damping of a violin is much influenced by holding it, as well as from variation in relative humidity. They came to results indicating that a slightly higher damping was preferred. That can be caused by the experience with the violins being more damped than we measure them. A pretty obvious explanation.

Jansson did measure this effect many years ago and show the resonances. In his work it seeme as the highs got a boost and the lows became more rounded and weaker.    

The played open string notes are louder than the same notes played on fingered strings.  This means that the player's relatively soft finger tips must add considerable damping.  

Attached is a plot of one of my violins with the open E string being bowed compared to the same note fingered on the A string.  The finger tip seems to add more damping on the higher harmonics.

I've sometimes gotten the impression in blind tests that there was more sound difference between two different players playing the same violin than the same player playing two different violins.

I used to attribute this to the different players having different bowing (bow speed, position, force) but now I suspect that the physical properties of the player's finger tips also plays a roll.

We like to investigate the violin wood properties and violin design but maybe the player's finger tip properties are more important: finger tip diameter, flesh stiffness, skin callus thickness etc.