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I started to thickness a practice top this weekend, and am using the same way of measuring Young's Modulus as the Gore/Gilet book explains. I believe that I am on the right track at reading the frequencies from the tap testing that I did on the halves of the top, but want to run it by some other people that have used this method to make sure that I am reading it correctly. Here is the woods data, I believe it is Lutz Spruce:

Length 547 mm
Width 206.50 mm
Thickness 4.32 mm
Mass 175.70 g
ρ (density) 360.1 kg/m^3

I've attached a spectrogram from each of the tap tests. The program that I'm using is Visual Analysis, and if you would use it, and would prefer to see the log file, let me know and I can send it over. My findings for the frequencies were:

fL 80.08
fC 127.80
fLC 50.40

They don't seem unreasonable to me, but I am untrained, so any help or pointers would be appreciated. Thanks!

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Jason McGowan
M&S Guitars
_____________________________
United States of America, looks like another silent night
As we're sung to sleep by philosophies that save the trees and kill the children....
Casting Crowns

Using those numbers, I get the following Young modulus values:

El = 10,495 MPa
Ec = 543 MPa
Glc = 761 MPa

For comparison, I tested a piece of Lutz from Shane and here were the results:

El = 12,383 MPa
Ec = 852 MPa
Glc = 892 MPa

So not that far apart. For the record, I've never verified my spreadsheet against anyone else's calculations.

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Formerly known as Adaboy.......

Those are really close to the numbers that I arrived at as well:

El = 10.43 Gpa
Ec = 0.54 Gpa
Glc = 0.76 Gpa

So Darryl, does it seem to you that I am reading the spectrogram correct as to which frequency spike is the correct one for the long, cross, and long/cross frequencies? In the images of spectrogram, the frequency spike that I have chosen as being the correct one is marked with the cross-hair. I had a hard time suppressing the other nodes while testing any given mode.

_________________
Jason McGowan
M&S Guitars
_____________________________
United States of America, looks like another silent night
As we're sung to sleep by philosophies that save the trees and kill the children....
Casting Crowns

I think you probably have those modes right, but, as you say, there's room for interpretation. I'm particularly interested in the 'notch' at around 46 Hz in the first chart that shows up as a peak in the third one, where the 49 Hz peak from the first chart is showing up as a dip. It's possible that there's something going on there, and it would be nice to know what it is. I can think of some possibilities. The most likely ones are that you don't have you holding point quite right, or that there's another mode close in pitch to that one, and the two are coupling. There's a similar bit of confusion at around 120 Hz.

I think this points up that every measurement has it's limits, which need to be understood. As I say, it's likely that you've gotten things right in this case, but there could be circumstances where the outcome would be less assured. One way to check this is to cut the piece down a little, either in length or in width, and test it again. If there are overlapping modes, altering the aspect ratio of the piece will change the frequency relationships, and move the peaks relative to each other. If the length stays the same, and the 49 Hz peak is still in the same place, but the 'notch' has moved, you have some assurance that the 49 Hz peak is indeed the lengthwise bending mode, unperturbed by anything else. If both peaks move, theres some more sleuthing to be done.

I've always used Chladni patterns to find these modes. In part it's simply a matter of having the means to do so when I didn't have a computer (let alone one that could do FFTs in any reasonable time ). An advantage of the Chladni method is that you can see it when there's another mode coupling with the one you want: the shapes are messed up. It's not uncommon, for example, for there to be a torsion/bending mode in the same frequency range as the crosswise bending mode of a guitar top half. The torsion/bending mode will have a node line along the grain up the center of the peice, and two crosswise lines near the ends. When this is close to the crosswise mode frequency the latter can assume a 'fish' shape: rounded outward at one end, and inward at the other. In some cases you'll get 'left' and 'right' fishes, at different frequencies. This is obvoius when you can see the mode shapes, but not so much in a spectrum chart, where it would be likely to show up simply as features in the shape of the peaks such as I've pointed out.

There's a further limit that has nothing to do with that, but should be understood. As the late Dana Meadows pointed out in her book 'Thinking in Systems', all models are just models; they are not reality. The models that are used to set up the equations that we solve to find the E values are simplifications, and don't take some things into account. For example, even if you've got a narrow beam vibrating along it's length, the restoring force is not simply from the Young's modulus along the grain. There are, at least, shearing forces set up within the material. A complete model would take those into account, but it would also require data from at least one other mode, in which shear predominates, to factor it in. This sort of model was treated is a series of articles in the Catgut Acoustical Society 'Journal' by McIntyre and Woodhouse: "On Measuring Wood Properties", that appeared in issues in November of '84. and May of '85 and '86. Without the further data and analysis the numbers we get from out simple models are only accurate within about 10% or so. This is, of course, 'good enough' for us: that implies that you can hold the thickness to within 3% or so, and most of us don't do that. Still, it's good to understand the limits of the techniques we use.

These peaks were very peculiar to me as well. The only thing that I can think of that could have attributed to this, other than me probably not holding it 100% correctly, is that the panel that I was testing did have a few small cracks in it. One from each end (caddy corner from each other), about an inch or so long. I got this top as packing material from Shane at High Mountain, and figured it would be a good top to practice this on. I tried to super glue the cracks closed, but for some reason, it just wouldn't hold. Maybe I was using the wrong kind of super glue.



Is there a mathematical way to be able to tell where to hold and tap to get the proper response? I had a real problem getting the cross frequency to come in clear. It seemed if I held it in one place, I would get one reading, and when held just even an inch closer to the center of the panel, I would get completely different readings.



So next time I run into a situation like this, where I can't get a clear reading on the cross frequency, I should rip a few millimeters off of the panel, and check to see which one of the frequency spikes do not move? That would give me a better guess as to where the cross frequency is, correct?



I plan to use Chladni patterns as well, I just haven't had the chance to build any sort of testing rig for this as of yet. I need to do a little more research on this so that I can get into it, and learn more about it.



This is all really good information, Alan. I really appreciate your responses. I can always count on them to be useful, and well thought through.

_________________
Jason McGowan
M&S Guitars
_____________________________
United States of America, looks like another silent night
As we're sung to sleep by philosophies that save the trees and kill the children....
Casting Crowns

jmc2010 asked:
"Is there a mathematical way to be able to tell where to hold and tap to get the proper response? I had a real problem getting the cross frequency to come in clear. It seemed if I held it in one place, I would get one reading, and when held just even an inch closer to the center of the panel, I would get completely different readings. "

For a uniform rectangular panel in which the modes are well separated in frequency, the hold points should be 21% of the way in for the lenghtwise and crosswise bending modes. A fifth of the way in is usually pretty close, and you adjust from there. An inch in or out on the crosswise mode is a lot. Plates with runnout will have the node lines for the lengthwise bending mode come in at an angle, so they will be higher on one side, and lower on the other, than they 'ought' to be. Variations in the crosswise stiffness, due, say, to ring angle changes, can shift the node lines for the crosswise bending mode.

Cracks can give you all sorts of problems.

"So next time I run into a situation like this, where I can't get a clear reading on the cross frequency, I should rip a few millimeters off of the panel, and check to see which one of the frequency spikes do not move? That would give me a better guess as to where the cross frequency is, correct? "

Making the panel narrower will raise the pitches of any modes that bend in the cross direction, and any twisting modes as well, most likely, but should not effect 'pure' bending modes along the grain. Making the panel shorter will raise long-grain bending frequencies, and probably the torsional modes as well.

There's a special case that you'r unlikely to run into with guitar top halves, bu you never know: the one where the lengthwise and crosswise bending modes come in at the same frequency. Basically, they won't, even if the math tells you that the travel time for a bending wave along the plate is the same as it would be for one across it. What happens in this case is that the ods couple, due to the 'Poisson's ratio' of the material, and as Tervor points out, coupled modes kick each other apart. This is the origin of the well-known 'X' and 'O' modes on violin plates. I covered that in my series on 'free' plate tuning in American Lutherie, which is reprinted in the first 'Big Red Book'. The interesting thing there is that if you have perfectly 'closed' O and X modes on a rectangular plate, the average of the two mode pitchers will be what the lengthwise and crosswise frequencies should have been, while the difference between them wil be a measure of the strength of the Poisson's ratio of the wood. Usually with guitar top halve, by the time you cut them down to get the modes to close, you can't use the pieces any more because they're too short. If you see the node lines curving, even when the modes are not perfectly closed, there's some Poisson ratio getting into the measurement.

Isn't this FUN?

So, you are saying the the node for the long and cross both will be in the same location, or very close to each other? Maybe this was part of my confusion and one of the major reasons that I was having a hard time getting a readable cross mode. Another thing that I was having an issue with was that I assumed that the other modes wouldn't be visible in the spectrogram. I thought that they would either not be there, because of not being excited, or that they would be canceled out by the current mode being tested. It took me a while to realize that this wasn't exactly the case. They may not be as excited, but it seemed really hard not to get them to read at all, if not impossible. Unless, of course, I was just doing it all wrong.



Gotcha! I will keep this in mind if I have any issues with the actual build top that we'll be doing this week.



Yes, actually! I feel like if I can truly learn and understand what makes all this stuff work, I will be able to make an exceptionally great sounding instrument. Which, of course, is the whole point.

_________________
Jason McGowan
M&S Guitars
_____________________________
United States of America, looks like another silent night
As we're sung to sleep by philosophies that save the trees and kill the children....
Casting Crowns

Would someone mind posting a photograph of their test setup? To include a top in it?

Thank you,

Mike

Bump

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Max Bishop
Brighton, Michigan

There are people on this forum that are probably a lot more qualified to show their test rigs, but I am in the shop for the rest of this week/weekend, so I'll get some pics of what I have and post them.

Jason

_________________
Jason McGowan
M&S Guitars
_____________________________
United States of America, looks like another silent night
As we're sung to sleep by philosophies that save the trees and kill the children....
Casting Crowns

Bump

_________________
Max Bishop
Brighton, Michigan

I apologize Mike, I didn't get any photos of my setup this weekend. Humidity was near 90% most of the weekend, so that put an end to most of my work. Ended up making jigs and working on a few necks instead.

Jason

_________________
Jason McGowan
M&S Guitars
_____________________________
United States of America, looks like another silent night
As we're sung to sleep by philosophies that save the trees and kill the children....
Casting Crowns