Myth/science In Lutherie

[speal]

A real myth or perhaps scientific theory that I would love to be broached:

THE SPEED OF SOUND

Basically, sound energy propagating through elastic materials varies with the material density. This will obviously affect the tone of our instruments as resonances, internal reflections and phase cancellations will all come into play here. I understand that acoustic instruments are much better designed in terms of wave propagation for obvious reasons. Electric instruments however, seem to have a degree of faith in how the instrument will sound. A Les Paul is what I perceive to be a "slow" instrument in terms of propagation whereas a Tele is "faster".

Interesting variations which will undoubtedly affect this aspect of solidbody design are:

- dense neck laminations on neck-through instruments allowing vibrations to be unmolested by changes in material density between nut and bridge

- heavy top caps "tightening" the body sound slightly

- necks with differing fingerboard woods

- differing nut materials

As mentioned, a lot of this is taken for granted in lutherie and general instrument lore - how does it translate in the really real world however?

I'll have to tackle this one with a pencil and paper in a few minutes. There could be some interesting consequences of using similar density woods in a laminated neck... it may end up being nothing though.

[psw]

Seriously though, those are just another take on Fatheads - brass plates you attached to the back of your headstock. Did anyone ever use those?

Adding mass to the headstock does seem to change tone and sustain. I haven't used these devices, but most will have found a change in the resonance of a neck when changing tuners from a cheap open type to a weighty closed, diecast type of tuner for instance. You can get sinilar effects by pushing the headstock against something to dampen resonant frequencies that will interfere with a strings vibration.

But, hanging a chair or other weight, from a headstock will seriously unbalance a guitar. Such changes to a guitars resonance (the vibrations of the neck) may not itself be desirable anyway.

You do want a neck that does not exibit dead spots (carbon fibre and stout truss rods can help here) but in many respects I've come to feel, and it may seem ironic since I am involved in sustainers) that sustain is a little over-rated anyway...but I guess it depends a lot on what you want from an instrument. A lot of the character of an instruments attack and decay and general "tone" comes from the interaction of various resonances...

Anyway...a little off topic perhaps...interesting thread... pete

[speal]

Okay, so here's what I've got for the density issue in laminated necks:

Assumptions:

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1. String vibrations are transferred to two pieces of laminate at exactly the same moment (ie, the string slot in the nut is right above the join between the laminates).

2. The rule I derive applies only to open strings, as the contact point for vibration is at the nut.

3. Wave interference is said to be "completely destructive" when one wave is half-way through its period, while the other is just starting it. Adding these two waves together yields a straight line.

What I'm doing:

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In a set-neck or bolt-on guitar, the neck resonance will be transfered through a "point" (the joint). If a neck is made from at least two types of wood, can the different densities of the wood lead to destructive interference at this joint, and thus hurt the sustain of the guitar?

Okay, here it is:

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Two strips of wood (our laminates) run parallel, and are length L. This length is the distance from the nut to the neck joint at the body. The speed of sound transmission for our laminates is known (it can be looked up in a table).

Our frequency will be the same at all places (we'd hope: this determines the pitch of the string). Wavelength, however, depends on the density of the material that the wave is propagating through.

For destructive interference, L should equal n * l1 (l1 is the wavelength of our wave in the first piece of laminate. L should also be equal to (n + 1/2) * l2, where l2 is the wavelength in the second piece. One fundamental law of waves is that wavelength * frequency is equal to the speed of propagation(c1 or c2), so we can substitute this in:

n * c1 = (n + 1/2) * c2

a few steps bring us to this result:

n = 1 / (2 * (c1/c2 - 1) )

since n is some number of wavelengths in laminate 1, we can reuse the equation L = n * l1. By multiplying both sides of the equation by l1, we get this:

L = n * l1 = l1 / (2 * (c1/c2 - 1) )

And because wavelength * frequency = c, we get this:

L = c1 / (2f * (c1/c2 - 1) )

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Okay, lets plug in some numbers:

Frequencies:

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E = 82.41Hz

A = 110.00Hz

D = 146.83Hz

G = 196.00Hz

B = 246.94Hz

e = 329.63Hz

The highest frequency is going to give us the smallest wavelength, so we'll use high e to find minimum neck lengths for interference.

Speeds of Propagation:

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Rock Maple: 4200m/s

Honduras Mahogany: 4970m/s

Honduras Rosewood: 5217m/s

Beefwood (for comparison): 3364m/s

Let's try a neck with laminated magohany and maple:

L = 4970m/s / (2 * 329.63Hz * (4970 / 4200 - 1) )

L = 41.12m

Yes, 41 meters. So, clearly this isn't going to be much of a problem unless you're building a super-jumbo guitar.

Let's try a bigger difference in woods (the biggest I could find). Rosewood laminated with beefwood:

L = 5217m/s / (2 * 329.63Hz * (5217/3364 - 1) )

L = 14.37m

Oh, much better. This guitar only has to be 14 meters long....

So, clearly, this particular possibility for interference has no effect at the frequencies of regular guitar strings. I'll explore the possibility of interference between waves originating at the bridge and waves originating at the nut soon.

EDIT:

I thought I should add this bit of information. At a 25.5" scale, the reduction in amplitude due to interference with a mahogany and maple neck is around 1.5%. I can't say how much, but the neck's vibration doesn't account for much of the actual output of your guitar, so this 1.5% doesn't lead to a noticible reduction in guitar volume. Thank god, since this would be one more thing that could lead to dead spots along the neck, assuming the same rule applies to fretted notes (it's probably close).

Edited December 23, 2006 by speal

[westhemann]

Does a fat person have more sustain in his guitar that skinnier one ?

The answer is yes.

just get one these http://www.stringsdirect.co.uk/Catalogue/V...x?productId=406

and you don´t have to eat so many donuts.

if you are going to put that monstrosity on your headstock,you might as well just put an allen wrench bracket on the back of the headstock.it is made of metal and at least has a real purpose

http://guitarpartsdepot.com/Merchant2/merc...loyd-Rose-Parts

[Jon]

"Tone is in the fingers"

There are plenty of professional musicians that will agree with you on this. I certainly do as a bassist that uses several different finger techniques, it's all about the technique!

[Prostheta]

Awesome work there Speal - I only wish I had pushed my physics study to the point of being able to apply it myself although I can follow the track you're working on. Am I right in thinking however, that the harmonic overtones will be affected to a greater degree than 1.5% through their shorter wavelengths?

[fryovanni]

Speal, You seem to be very sharp with your Physics. Sometimes you guys make me feel pretty inferior mentally , but I sure like having you guys around the board .

So I have a couple things that are jumping out at me and maybe you could let me know if these could be valid concerns(with regards to your speed of sound calcs).

First of all would we anticipate 329.63Hz to be the high end of the frequency range on an electric guitar.

The speed of sound transmission for our laminates is known (it can be looked up in a table).

When you looked this up are there other variables that modify the speed of sound transmittion through wood?

Assuming your 1.5% Maximum reduction is the case, and lower reduction as frequency is reduced. How would this effect the way we percieve the change in sound. Given that humans do not percieve frequencies across the audible spectrum evenly.

Since Harmonic overtones have been brought up. Very slight changes in overtones can make a very large difference in percieved tone or "voice" of an instrument. How would we relate the significance of this small change as it relates to overtones?

A question and observation. I am very familiar with acoustic sound boards and the way different woods sound/ring. Moisture content of wood greatly reduces speed of sound transmition in wood. I have tapped soundboards with moisture contents in the 18% range(pretty wet), and then again after they have reached equalibrium(around 8% moistire in my shop). There is an undeniable change in the way they sound/ring. Would your theory be that the speed of sound through the wood is not changing the sound of the wood? Obviously this is not a large or long piece of wood I am talking about. What would your thoughts be.

Peace,Rich

[speal]

First of all would we anticipate 329.63Hz to be the high end of the frequency range on an electric guitar.

Am I right in thinking however, that the harmonic overtones will be affected to a greater degree than 1.5% through their shorter wavelengths?

The frequency I used, 329.63Hz, is the high e string frequency. I used this because the formula I derived only accounts for open strings. The thing I overlooked is that harmonics also vibrate along the full length of the string, and can be used, and these harmonics are the overtones you hear when you pluck an open string.

Octave harmonics are the most audible, and occur at frequencies that are powers of 2 * the open string frequency. This corresponds to a length that is one over that power of two. So, the first octave harmonic occurs at 1/2 the string length, and is twice the frequency of the open string.

On the maple/mahogany laminated neck mentioned above, an amplitude reduction of 10% occurs at a frequency of 4185Hz (scale length of 25.5"). This is around 16 * the frequency of the open B string. 16 = 2^4, so this is four octaves above the open B string. Not all harmonics occur as natural overtones, but it's safe to assume that an octave harmonic would occur as an overtone.

As you increase the distance between the fundamental pitch of the string and an overtone, the amplitude decreases. 16 * the fundamental frequency is going to be MUCH quieter, so this reduction, although significant, may not be audible because this overtone is so far from the fundamental frequency.

I'm going to do some more in-depth work on this problem, since you end up with some interesting interference between waves originating at the nut and the bridge. That, and resonance could have some interesting effects.

One thing I'm particularly interested in investigating:

Waves moving in opposite directions interfere and form standing waves, not unlike the vibration of a string. There are particular positions along the wave that will always be the peak amplitude, and others that will always have zero amplitude. I'd be interested to know if placing a pickup at a zero amplitude spot would sound different from a pickup at a higher amplitude location. Keep in mind this amplitude is for the body's vibration, not the string.

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As far as speed of propagation for sound through wood, there are many factors that could affect this speed.

1. Each piece of wood is unique. There are no concrete rules, since imperfections (including desirable ones, like figuring) can affect transmission speed, as well as natural variations in density/water content.

2. Sound propagates at a different speed for each frequency, as well. In a medium like air, the variation is so small for the audible range, we stick with a single value. In wood, the speed is significantly higher (by more than a factor of 10). The variation due to frequency may actually be worth looking into. I'll get some concrete numbers for this.

3. Tension on the wood will, with absolute certainty, affect the speed of propagation. Speed along the grain is much faster than across it, so the fastest propagating sound waves may follow the curved path of the wood grain if the neck is bent. When you're talking about small percentages in interference, this difference can be significant.

4. The width of a piece of wood will affect its resonance. At some frequencies, propagation along the width of the wood can lead to interference in the length propagation, effectively reducing the transmission speed.

5. Environmental factors like temperature, humidity, air pressure, etc... will play a role in sound transmission and resonance, so these may be worth looking at as well.

So, in the end, the problem becomes MUCH more complicated. Developing a good model will be difficult. Luckily, the wavelength of your low E string is around 10 meters when traveling through maple. This leaves a lot of room for error. My intuition tells me that laminated necks aren't going to have any real effect on the sound of the guitar. More important will be the relationships between bulk masses in the guitar, and their resonant frequencies. The contact area of the neck joint could really affect the resonance of the instrument as a whole. I'll have to brush up on some acoustics and look into this to give you a real answer though.

----------------------

A question and observation. I am very familiar with acoustic sound boards and the way different woods sound/ring. Moisture content of wood greatly reduces speed of sound transmition in wood. I have tapped soundboards with moisture contents in the 18% range(pretty wet), and then again after they have reached equalibrium(around 8% moistire in my shop). There is an undeniable change in the way they sound/ring. Would your theory be that the speed of sound through the wood is not changing the sound of the wood? Obviously this is not a large or long piece of wood I am talking about. What would your thoughts be.

This could be only due to the mass change. The relative volume is the same, but mass is greater, so density is higher. Water is also a terrible conductor of sound, so the sound waves may take jagged paths through the wood. Since the simplest look at resonance depends on the length of the longest and shortest possible "paths" for the sound, the change in humidity could easily change the character of the wood. You're not just imagining the tone difference either. Again, the water is probably the culprit. A slow sound transmittor decreases wavelengths, lowering the minimum frequency for interference. You'll lose more overtones as you introduce more water into the wood.

[fryovanni]

Speal,

Great responce. That is a scary mind you have there . I look forward to reading your findings. I may just have to have you look over an acoustic bridge I am working on for some possible ideas on improvements.

So to maybe through a little more fuel on this fire.

3. Tension on the wood will, with absolute certainty, affect the speed of propagation. Speed along the grain is much faster than across it, so the fastest propagating sound waves may follow the curved path of the wood grain if the neck is bent. When you're talking about small percentages in interference, this difference can be

Lets talk about another subject that comes up frequently. Grain orientation. As you mentioned speed along the grain is much faster. How much of a factor would orientation play on the sound of an instrument? obviously in relation to the strings a flatsawn neck would oriented parallel(cross grain in section), and a quartersawn would be perpendicular. Then you have the body to neck joint where orientaion could again vary. Do you think this would be an insignificant factor(take extream examples for comparison), or would it be such a small factor that it couldn't possibly be notable?

Peace,Rich

[westhemann]

stiffer necks seem to resonate better..imo

[speal]

stiffer necks seem to resonate better..imo

That's probably because of damping. A stiff neck will absorb less of the sound energy, and you'll sustain better. It's important to distinguish between resonance and sustain. Sustain is the length of time your guitar will continue to produce one particular note above a certain threshold of volume. Resonance has to do with your guitar's natural resonant frequency. This can determine the complexity of the overtones generated, and depends on design, materials, and environment. Good analysis of resonance takes a LOT of data, and a lot of complex math...so it's tricky to get it just right.

Oddly enough, resonance also affects sustain. If your guitar's natural resonant frequency (or one of them; it will have many) is near that of a note you play, this particular note will be louder, and sustain longer. It's not hard to observe this in an acoustic, where some notes will really ring out above the others. Feedback in semi-acoustic electric guitars is generally at the body cavity's resonant frequency as well.

As you mentioned speed along the grain is much faster. How much of a factor would orientation play on the sound of an instrument? obviously in relation to the strings a flatsawn neck would oriented parallel(cross grain in section), and a quartersawn would be perpendicular. Then you have the body to neck joint where orientaion could again vary. Do you think this would be an insignificant factor(take extream examples for comparison), or would it be such a small factor that it couldn't possibly be notable?

The chart I looked at showed that sound travels across the grain at a speed around 1/3rd that of the speed along the grain. So yes, this would make a big difference. Your open strings still have wavelengths beyond the scale of your guitar, but the first and 2nd octave harmonics will have wavelengths very near that of your scale length. At this point, a difference of an inch for pickup or neck-join placement could have a big effect on overtones, and thus the "warmth" of your guitar.

------------

Thanks for all the good feedback on this. The key to what I've been doing is to simplify the problem so it can be understood using very simple physics. Unfortunately, resonance and interference in any musical instrument is very complex, so a thorough treatment is a very involved process. I may end up writing a java simulation that combines some of the effects we've talked about. Unfortunately, this will have to wait until at least a few days after the holidays. I'm also going to be fitting in a through-neck guitar project. As a side note, would anyone see a problem with a 1/2" strip of cherry down the middle of a laminate maple neck? I haven't worked much with cherry, so I'm not familiar with it's strength or application to necks.

Merry Christmas!

[Prostheta]

It would be an interesting one for sure. I'm building two identical basses sometime this Spring but with a different base config between them both. One will have wenge neck laminations in a mahogany through-tenon and the other an ebony central lamination with some (insert wood here) laminations.

The perfect A/B test!