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freddieb
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PostPosted: Tue Nov 13, 2007 3:59 pm 
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Can someone explain the physics behind making a guitar string vibrate at a certain pitch?

What are the factors?

These are the factors that I can think of . . .

1. length of string
2. tension on string

Bit of a vague question I know, but I thought I'd ask anyway . . .

Thanks,

Freddie
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Rick Turner
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PostPosted: Tue Nov 13, 2007 4:04 pm 
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1) Unit density/weight measure

2) Length

3) Tension

Those three issues determine pitch...discounting string stiffness which moves harmonics sharper and sharper the higher up the harmonic series you go.


Google the D'Addario site. Great stuff there on tension gauge (unit density)
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Mike Mahar
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PostPosted: Wed Nov 14, 2007 12:54 am 
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More than you ever wanted to know about how strings behave is in a article by Al Carruth in the latest issue of the ASIA journal "Guitarmaker".



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Zach Ehley
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PostPosted: Wed Nov 14, 2007 3:51 am 
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Length, mass and tension.  For fellow enginerds who want to chug through some equations go to http://hyperphysics.phy-astr.gsu.edu/hbase/waves/string.html.  Its a good simple explanation without requiring a masters in mechanical engineering to understand.  Also there is a cool simulator that allows you to see the motion of the string based on where you pluck it.  http://falstad.com/loadedstring/
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Parser
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PostPosted: Wed Nov 14, 2007 4:56 am 
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The factors listed above are the main ones.

One often overlooked (from an engineering perspective) aspect of this type of vibration is the end conditions. I used to work for a company that designed shafts & such for turbine equipment and the stiffness of the bearings supporting the shafts have a very large effect on the vibration characteristics. Most engineering calculations assume that the ends are infinitely stiff (i.e. a perfect theoretical situation).

So...for guitar strings that tells me that the break angles and relief at the nut and the bridge are also pretty critical.


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Rick Turner
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PostPosted: Wed Nov 14, 2007 5:29 am 
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And most string engineering calculations assume the string to be infinitely flexible...which they're not. The lack of perfect flexibility at each end of the string (and in the string itself) is the basic reason for intonation compensation at the bridge.   The thicker strings are, the more they act as clamped bars, not one dimensional strings which is what all harmonic theory is based upon.
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Todd Rose
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PostPosted: Wed Nov 14, 2007 5:52 am 
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Recommended book: Fundamentals of Musical Acoustics, by Arthur Benade.

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Zach Ehley
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PostPosted: Wed Nov 14, 2007 6:54 am 
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When looking at vibration, engineering calculations are always wrong because they never take all variables into consideration.  We did finite analysis on a pump, a big big pump, which showed a natural frequency right at the operating speed.  We braced the heck out of the thing to move the resonance.  Low an behold it would have been fine in the first place and the bracing we did actually caused vibration contrary to the FEA.


Same with the string calculation.  There is no good standard for a guitar string model. Its not fixed or simply supported, but something in between.  Then the vibration will stretch the part of the string beyond the nut and saddle.  So its somewhat pointless to try to get it exact.  There are just too many variables to account for on a guitar to do a truly accurate calculation.  Follow the KISS rule.


The string is assumed to be infinitely flexible because if you ever exceed the yield stress, everything goes to pot in the calculations.  Unless you were refering to the flexability of the support point.
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Alan Carruth
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PostPosted: Wed Nov 14, 2007 7:04 am 
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As Mike said, I spent 'way too much time over the past three years or so measuring string vibrations, and figuring out what the h--- was going on. The conclusion I came to, in a nutshell, is that the usual physics book explanations are fine as far as they go, but all the _interesting_ stuff is in the non-linearities that require too much higher math for the usual beginner's books. That's why it took me so long: that level of math is beyond my skill and I wasn't expecting to see a lot of that stuff.

That said; yeah, you can calculate the fundamental pitch 'close enough' if you know the length, tension and mass per unit length. The partials will be progressively sharp if the string is on 'rigid' mounts; a solidbody guitar (but not a bass!) would be close enough for government work. Stings on guitars can do all sorts of weird things. and all of this assumes that the strings themselves are not too messed up; circular in cross section and so on.    
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Rick Turner
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PostPosted: Wed Nov 14, 2007 7:11 am 
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The other wild card is that the ends of the strings are not true nodes because of the coupling factors. Once you couple a moving string to a structure that moves, that structure starts acting like a non-linear function added to the string.   

Best to know the simple theory, and then know that all sorts of things interfere with that simplicity.
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Michael Dale Payne
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PostPosted: Wed Nov 14, 2007 7:32 am 
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[QUOTE=zehley]

When looking at vibration, engineering calculations are always wrong because they never take all variables into consideration.  .

[/QUOTE]

Being an engineer; Dependent on the exercises at hand, Failing to to take all applicable variance in to consideration would be a dereliction of the tack.

Now that said, there does come a point in time where you can continue to add variable that are not real world realistic.

If you are working with engineers that fail to take applicable variances into consideration then you need a new Engineering Manager.

30 some odd years in mecanicl engineering I have seen vary few cases where a part/structure failed because the engineer did not take know variances into consideration in their calculations. As an engineering product failure investigation team member almost every stress or catastrophic shock failure I have seen turned out to be product fabrication or usage errors.

The few times that I have seen engineering calculation errors to be directly linked to a failure it could be referred "bad info in= bad Calc's out syndrome" meaning where the data provided to the engineer was incorrect therefore the engineers calculation output is not up to snuff.

But I can say that engineers will look at all applicable variance when doing structural calculation. We take this stuff pretty seriously.
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Michael Dale Payne
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PostPosted: Wed Nov 14, 2007 7:34 am 
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Being an engineer; Dependent on the exercises at hand, Failing to to take all applicable variance in to consideration would be a dereliction of the tack.

Now that said, there does come a point in time where you can continue to add variable that are not real world realistic.

If you are working with engineers that fail to take applicable variances into consideration then you need a new Engineering Manager.

30 some odd years in mechanical engineering I have seen vary few cases where a part/structure failed because the engineer did not take know variances into consideration in their calculations. As an engineering product failure investigation team member almost every stress or catastrophic shock failure I have seen turned out to be product fabrication or usage errors.

The few times that I have seen engineering calculation errors to be directly linked to a failure it could be referred "bad info in= bad Calc's out syndrome" meaning where the data provided to the engineer was incorrect therefore the engineers calculation output is not up to snuff.

But I can say that engineers will look at all applicable variance when doing structural calculation. We take this stuff pretty seriously.
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Rick Turner
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PostPosted: Wed Nov 14, 2007 7:41 am 
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You can also spend so much time on over-engineering, studying, and documenting something like a guitar that you simply run out of money...   There is not a $5,000.00 engineering budget to spend on each $4,000.00 guitar...
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Michael Dale Payne
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PostPosted: Wed Nov 14, 2007 7:52 am 
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been there done that not on guitars but on pumping units


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