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I seem to remember that Bob Benedetto made an archtop out of pine in his book. Acording to him it came out very nice. I bet in the hands of a skilled luthier, just about any wood would do.

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Joe Breault
Merrimack, NH
Perpetual novice

You asked for it!

Basically, so far as we know now, the acoustically important parameters are the lengthwise and crosswise Young's modulus of the wood, the associated damping factors, and the density. It's possible that one or more shear moduli are also important, as they have been found to be so on violin top wood, but that's open for debate on guitars.

Daniel Haines did a rather good study of wood properties some years ago, and published an update of it in the Catgut 'Journal' a few years back. Much of Dave Hurd's book is involved with testing the stiffness of tops, and he does go into the methods used, which Haines did not. Fortuneately, I learned the method that Haines used from Mort Hutchins. There are other ways of getting the information, but this works well for what we want.

One problem in measuring the Young's modulus of wood is cold creep: when you laod a sample it deforms continuously. Thus the easy method, of loading a beam and measuring its deflection, is not as useful on wood samples as one would like. The deflection increases over time, and you usually end up geting lower values for the Youngs modulus than you 'should'.

If you know the length and thickness of a beam and the density of the material you can use the frequencies of the vibration modes to calculate the Young's modulus. The restoring force when the beam is bent comes primarily from tension and compression of the surfaces. This eliminates any 'cold creep' problems, and also gives the opportunity to find the damping factor, by observing the 'half power bandwidth'.

All you _really_ need to do is support the piece at the points where the node lines for the lowest bendig modes cross, tap it, and record the sound. This can be Fourier transformed to find the pitches of the lowest modes, and the bandwidth can be read directly from the FFT plot. Knowing the size and mass of the piece you can plug into the appropriate equations. All you need, then, is a computer with a sound card, a microphone, an accurate scale, and some software.

Using a signal generator might be a bit more accurate. You need some means of driving the plate and a way to detect the vibration, neither of which adds mass or stiffness to the plate or interferes with the other. I stick a little rare earth magnet to the plate and drive it with a coil from an old relay, 'pushed' by my signal generator. I 'listen' to it with my RadShack dB meter, which makes it easy to get the 3dB down points. Even Davis drives his plates with a speaker, and uses an electric guitar pickup to sense a little bit of steel string stuck to the end of the plate. He just plugs into a DVM and reads out the AC voltage of the pickup.

The relevant equations are:
Young's Modulus (E) = 0.946 *rho*(fo^2)*(l^4)/h^2
Q=fo/(fh-fl)
C=sqrt(E/rho)
R=C/rho

Where:
rho= density
fo= peak resonance frequency
fh= frequency above resonance where the amplitude is 3dB down (70.7%) from max
fl= the low -3dB frequency
C= the speed of a compression wave through the material
R= the 'radiation ratio', proposed as a figure of merit by Schelling for violin wood.
(from an article by Mort Hutchins in the CAS 'Newsletter' #40, Nov. '83)

All units in mks system!

There has been a lot of discussion about that whole 'figure of merit' thing. Most makers and researchers agree that what we'd like to make is the lightest possible top plate that will hold up under the string load. This gives you the loudest guitar, all else equal and, as has been said:"Give 'em volume and they'll hear tone!". Schelling's 'radiation ratio' makes a lot of sense on violins, where the structural demands are different. For guitars I think any FM wil have to include, at very least, the lengthwise Young's modulus. We're going to have to figure out how much of a _structural_ contribution the crosswise Young's modulus makes, aside from it's obvious _acoustic_ role. There is also room for debate about the importance of damping. Burns has proposed Q*E/D (Q times an average Young's modulus, over density) as a FM. However, Wright found _no_ perceptible difference in his computer model beween synthesized guitar sounds with widely varying Q factors. Even though I don't totally agree with him it does rather place the burden of proof on those of us who think of Q as important.

Suppose you want to make two tops that weigh the same and have the same _stiffness_, starting with woods of different E and rho values. For purposes of discussion we'll say you have a 'light' European top with a density of about 330 kg/m^3 and lengthwise E of 7500 megaPascals, and a redwood top with a density of 500 kg/m^3 and E of 15000mPa. (these are values very close to those of some tops I've got) The Euro top has 2/3 the density of the Redwood, so if (for whatever reason) we decide that the Euro top will work at 3mm thick, then the Redwood can only be 2mm thick to have the same weight. However, the stiffness will be proportional to the Young's modulus times the _cube_ of the thickness, so the Euro top will have a stiffness proportional to (3*3*3*7500)=202,500, while the redwood top of the same weight will be (2*2*2*15000)=120,000! Despite having much lower 'stiffness' the Euro top comes out lighter because of it's lower density. In fact, to achieve the same weight the ratio of Es has to go as the cube of the ratio of densities, and I think that wil have to be a factor in any figure of merit for guitar top wood. Note that Schelling's 'radiation ratio' has at least got rho squared in it, so that's a start.    

A couple of caveats:
These calculations assume 'pure' lengthwise and crosswise bending. If the aspect ratio of the plate is such that the lengthwise and crosswise modes come in at somewhat similar frequencies this will no longer be the case, and the properties you calculate will be 'mixed' to the degree that the bending is 'mixed'. This can also happen if there is somefeature of the wood, such as a knot or other 'wave' in the grain that causes the node lines to bend. This is one reason Haines and Hutchins liked to test long, narrow strips.

Another confusing factor is radiation loss, which adds to damping. Something as wide as a guitar top half can put out a certain amount of sound even at very low frequencies, and this is a 'loss' as far as the test is concerned. We're really looking for _internal_ losses, and sound output is hard to take into account. Once again, this is an argument for using narrow strips.

For that matter, there are likely to be losses to supports, such as foam pads, particularly if those are not carefully placed. I have noticed that simply moving my hand near the plate as it vibrates can cut the amplitude, and it would be wise, if possible, to work out some way of mounting them so that they are at least 1/2 plate length away from any support, such as a table top. (note that I did not do that on my tests)

In short, it's hard to get really accurate data. I'm figuring in my case that anything within 5% is 'identical' for all practical lutherie purposes. As always, just because your calculator runs things out to six decimal places, don't assume those last three or four mean anything.

Some useful articles are:
Schelling, "Wood for Violins" CAS NL#37
McIntyre and Woodhouse, "On Measuring Wood Properties" Pt I, II and III
              CAS 'Journals' 11/84, 5/85 and 5/86
Haines, "The essential mechanical properties of wood prepared for musical instruments"
              CASJ 11/00
Rodgers, "The effect of elements of wood stiffness on violin plate vibration" CASJ 1.1 pp2-8 May88

Whoops, one other thing:

All tests that involve measuring vibration assume that the resonance involved is 'isolated': that there is no other near it in frequency. This is part of the thing with the lengthwise and crosswise bending 'mix' I mentioned. You can also get into trouble measuring the Q value of one or another mode if there's a resonance nearby. In some cases, when trying to find the 'high' 3dB down point on some tops I couldn't do it because there was another mode right 'on top' of the one I was looking at, and you'de run up that peak before you'd dropped 3dB from the other mode. Oh well.

Oh yeah...

It's tempting to run the tests at very low power, to minimise the amount of radiation loss. I don't think it really matters, and it gets you into another problem if you're using a dB meter to 'listen': the signal/noise ratio. No place is really 'quiet', and when you have the meter set to a low range the background noise will be close to enough to get it to register. This doesn't effect the reading of the peak frequency much, but the 3dB down points will be farther apart than they 'should' be because of this so-called 'stochastic noise'. Just another little source of error.

Thanks Al
I've got to digest this. I do have questions.

John

Wow... ever think about writing a book about all this stuff?

Very interesting... thanks.

I too will have questions after I spend some time thinking.

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Brock Poling
Columbus, Ohio
http://www.polingguitars.com

Alan...that is exactly the type of info I was looking for. What a succinct and (believe it or not) very understandable description of all of the factors that are in play.

Thanks

Alan
Regarding cold creep. If you conduct a deflection test, (since I don't have the equipment right now and probably won't in the forseeable future) and do that fairly quickly can you get valuable information from that test. Is there not some way to "factor out" the effects of cold creep given that all pieces of wood do it to some extent.

Secondly. Since in the real world of a guitar top cold creep is a given, what about assessing that factor during the testing of top wood.

   Finally, I really did like the example of the two tops that showed a lighter stiffer top resulting from the less dense of two materials. But, do you have any numbers that define acceptable parameters for a deflection test that a not_so_geared_up more intuitive builder like myself could use as guidelines for evaluating tops. I am doing deflection tests and recording my own numbers, but would like to know if anyone has a collection of data I could tap into.

Thanks very much for the time you have spent on this topic.

John

Al,
Thanks, I think that’s pretty interesting. I also go through something similar, but I don’t do the Q thing. I find it really helpful in grading wood.
I was chewing on your comment on static testing and cold creep last night some and I’m not sure about it. I must confess I do static testing and I think I get very valuable information from it.
I think either way works as long as you are consistent with your method. The speed of sound “C” in your equations above I think have the biggest impact for us. Just my opinion. So any method I use to obtain E as long as it’s repeatable, will accurately grade my wood in terms of stiffness and speed of sound (assuming I have a good scale) amongst other pieces in my wood stash that I’ve done the same repeatable process on. The key here is repeatability not static vs dynamic. Neither method will actually tell you the exact modulus as there are lots of variables and the systems are not calibrated. I would have a hard time selling wood certified to a certain modulus to a company like Boeing (if they bought wood) based on either method don’t you think?
It looks like John also beat me here on the cold creep issue as those are my exact thoughts as well. It takes me about 30 seconds (maybe less) to do a static test. So I’m pretty sure creep doesn’t enter in. It’s certainly a factor on the guitar however. I also have pieces of wood I use as a calibration standard just to make sure everything is the way I think it suppose to and nothings funny.
I’ve included a picture of my set up for testing braces. I use 2 gallons (not one as shown) for my weight. The government is nice enough to assure the quantity so it makes a very repeatable and inexpensive weight.
I would encourage people to try this, the important thing is repeatability. Almost all the wood is usable but it helps to define what shape it should be and where to use it. I use all my lower modulus pieces for the finger braces on the perimeter and the high modulus pieces for the X.
I’m interested on hearing others thoughts on this. I’m not trying to start an argument over which testing is better.

_________________
Jim Watts
http://jameswattsguitars.com

Al and others, regarding the cold creep during measurements, here's what I've found. For nearly all samples, I find that the measurement reaches a maximum and stays there, at least for the duration of the measurement, which typically is not more than 20 seconds. Also, the sample returns to zero consistently, unless using very heavy weights. Once past a certain weight limit (the wood's proportional limit?), though, the sample WILL creep, and will not return to zero completely.

Despite limiting my measurements to the "linear zone" in order to avoid understimating Young's Modulus, my deflection tested strips consistently come in at a lower Young's Modulus than when tested acoustically. When running the 0,2 mode on the same strip samples I get values from 2%-20% higher.

From Al's note: It's possible that one or more shear moduli are also important, as they have been found to be so on violin top wood, but that's open for debate on guitars.

I can't say for actual instruments, but during deflection testing the shear modulii appear to be of some importance. In a discussion with David Hurd, he explained that there is one often neglected prerequisite regarding the dimensions of the test sample. For shear modulii NOT to affect the measurement to any great extent, the height of the test sample has to be very small in relation to the length. Off the top of my head (this could be inaccurate), I think the ratio was 1:30. With increasing height-to-length ratio the effects of shear modulii become apparent during deflection testing as an underestimation of Young's modulus.

This information is addressed in David's Book and on his website as well if I remember correctly. Unfortunately I don't remember the references for this information, but I'm sure David could cite them.

David couldn't conclusively attribute my discrepancy in deflection-tested-numbers to acoustically-tested-numbers solely to the effects of shear modulii with any degree of certainty. But, both David and I leaned toward trusting the acousitc measurements more, and thought the interaction with shear modulii could be a plausible explanation. I have not yet conducted a deflection test where the 1:30 criteria is met, so I can't say if that would put deflection testing more in line with acoustic testing.

So, at least for increasing the accuracy of deflection measurments, it seems like the effects of shear modulii are worth looking into.Pete Licis38545.5231828704

Thanks all, for amendations and corrections.

As Pete said, so long as you are static testing in the same way every time, and don't run off for a cup of coffee between loading and measuring, you're probably getting consistent numbers, and that's what's important here. Haines went with the dynamic test as being somewhat more accurate, and you do usually get lower E numbers with the static one for whatever reason.

Dave Hurd gave some 'acceptible' deflection numbers in his book, iirc. I loaned out my copy to a student so I can't look it up. The most useful one, in some ways, was the 'string load after assembly' test, but then, of course, it's too late. I confess to not doing too much of this material testing until recently, and I'm still getting up to speed myself. Dave's the expert.

I think the _most_ important things are to try to think of something that makes sense to measure, based on your own understanding of the way the guitar works, and then to come up with a simple and reproducible way to do the measurement and record it. If it's reproducible you can at least trust it, even if you're not coming up with numbers that mean anything to anybody else ("I hang this brick on a one cubit long piece that's 6mm by 3/7" in cross sction, and it goes to the second scratch mark I made on the wall"). The advantage of doing standardised measurements with (whatever) 'normal' units is that we can communicate them to each other, if we want to. If it's not simple you won't do it. You'll find out if it's a valid measurement (and, thus, if you really do know how the guitar works!)when you start seeing things that correlate in the instruments you make: all the ones with deflections greater than a certain number had the bridge fly off and kill the cat, so now we know how much deflection we can get away with (and where to get cats). If you don't record it you _will_ forget it.

Somebody said that we're in the 'naturalist' phase of stringed instrument acoustics: we don't really have many good theories yet, and we need to gather a lot more data before we can come up with one. At some point some Darwin will look at the data and realize there's enough to tie together with a theory, and then we can spend the next couple of hundred years arguing over whether it's blasphemous or not.