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A question of physics..

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Narn
 Narn
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Greetings. As my mind wandered this morning (lots of empty space to do that) I found myself wondering about string mass and diameter and the relation to pitch these influences have.

We all know that the larger strings on a guitar have a lower pitch that the smaller ones. Common sense, right. My question is whether or not that difference is related to the mass of the string, or the diameter of the string? If we have a given amount of energy imparted to strings of equal length will strings of the same mass, regardless of the size of the string, produce (approximately) vibrations of the same frequency ( assuming the difference in materials has a neglegible effect)? Or will the larger diameter string produce a lower tone regardless of mass?

Why?

Anybody have any thoughts?

"You want WHAT on the *&%#ing ceiling?" - Michelangelo, 1566


   
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Call_me_kido
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wow thats way out there


   
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spacedog03
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I'm thinking mass plays a bigger factor than size. Just a guess. I'm sure somone else will have a more informed opinion.


   
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Arcmage
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I think you can find your answer here http://www.noyceguitars.com/Technotes/Articles/T3.html


   
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Distortocaster
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Umm, I think it goes something like this:

Sound pitch is directly related to the frequency of the string's vibration (the number of oscillations per second). Since thicker strings have a higher mass, their vibration frequency is lower (because of inertia).
Think of how a chain and wrecking ball oscillate 'slower' than a pebble tied to a string.


   
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greybeard
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I'm not a physicist, so this is pure guesswork.

Diameter will play more part in pitch than mass IMHO. Take a piece of string and stretch it - pitch is determined by length and diameter.

Mass, on the other hand, will determine sustain - the more mass, the more potential energy and. therefore, sustain.

I started with nothing - and I've still got most of it left.
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Distortocaster
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Mass, on the other hand, will determine sustain - the more mass, the more potential energy and. therefore, sustain.

Now when it comes to guitars, sustain depends mainly on pickups (or resonating chamber if we're talking acoustic) and the elastic properties of the string's material.

Classical nylon strings have less sustain than acoustic steel ones.


   
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NoteBoat
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What a cool question!

Being fascinated by physics, acoustics, and of course, music, I set out to research this one....

The pitch of a string is related to three factors: mass, tension, and length.

We already know about the length part (at least intuitively), because when we fret a note, we're not changing the mass, and not changing the tension very much, but we're changing the length of the vibrating portion... cut the length in half (the 12th fret) and you double the frequency (the octave).

The relationship to tension is exponential... if you want to change the frequency up one octave, tension must increase 4 times, to go up two octaves, 16 times, and so on. Since the tensile strength of string material is quickly exceeded, the string breaks before you can go up very much... so we have to use a string of different mass.

The relationship to mass is direct: wave velocity, or frequency, is equal to the square root of (tension / (mass / length)). Double the mass, you halve the pitch. That's why thinner gauge strings are easier to bend - the reduced mass means you have to lower the tension for the same pitch... reduce the gauge 20% (go from .010 to .008) and you'll lower the tension 20%

Pitch isn't related to string diameter at all, except through the relationship to mass. Nylon strings have lower mass at the same diameter as steel, so the strings must be thicker to produce standard tuning - otherwise we'd need to raise the tension too high for the material.

Guitar teacher offering lessons in Plainfield IL


   
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Musenfreund
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I've found that pitch remains constant though both my diameter and mass have grown as I've aged.
Oh, you meant the mass and diameter of the strings. Never mind. :oops:

Well we all shine on--like the moon and the stars and the sun.
-- John Lennon


   
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Narn
 Narn
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(Noteboat, I was typing this response at the same time you were answering. It seems redundant now, but I'll leave it up.)

Ah Ha! Now everyones wondering.

In any event pehaps I should clarify.

In my original post I suggested we ingore materials for the sake of keeping the question simple. We know of course material will have an effect, but for the sake of this question let's play stupid and ignore that. I was slack and should have said we're doing this experiment on an acoustic only, so pick ups aren't a concern either. We are using the same guitar for each test, in the same location, with the same humidity.

With all other things being equal. What effects the pitch of strings of equal legnth? Is it detirmined by mass or the string or diameter?

I am further assuming the tension on each string is the same.

1) If we make a set of strings in which two strings of equal mass have different diameters, which of the two will have the lower frequency? Why?

2) If we make a set of strings where two strings of the same diameter have different masses which will have the lower frequency? Why?

It seems to me, with no experimentation to back this, that when the mass is unequal the more massive string will have lower frequency per unit of energy input. Since frequency is detirmind by "speed" insofaras how fast something vibrates detirmines pitch, it would seem that, per unit energy input, more massive strings would vibrate slower. Thus a lower pitch.

If you wonder why I wonder it was just a musing on how string makers come up with their product. If mass is the detirming factor in pitch you could have all of you strings the same size, but varying in mass. If mass has a significant affect could you not then put any string at any location and acheive the correct pitch by use of tension alone? Wouldn't that look funky?

I gotta find something else to think about at work.

"You want WHAT on the *&%#ing ceiling?" - Michelangelo, 1566


   
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Dan Lasley
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Mass, on the other hand, will determine sustain - the more mass, the more potential energy and. therefore, sustain.

Now when it comes to guitars, sustain depends mainly on pickups (or resonating chamber if we're talking acoustic) and the elastic properties of the string's material.

Classical nylon strings have less sustain than acoustic steel ones.

Sustain is determined by how well the guitar keeps the vibration energy in the string. An acoustic guitar works because the energy is transferred from the strings to the body. Careful design allows that thin little string to vibrate the large surface of the body to create a relatively loud sound. This drains the energy from the strings, so there is less sustain. Compare that to the sound of an unplugged electric guitar. This is also why acoustics usually have heavier strings than an electric. Your strumming puts more energy into the strings, and the extra mass creates more momentum, allowing the strings to vibrate longer.

In an electric guitar, the frets and bridge design determine how "perfect" the vibrations are. The body and neck determine how much vibration is shifted away from the strings. Some people argue that a neck-through design will have better sustain, as there is no neck joint loss. As mentioned above, there is some loss due to the pickups travelling through the magnetic field of the pickups. This should only be a factor if your pickups are extremely close to the strings, or you have very "hot" pickups. As with the acoustic, heavier strings will tend to have more sustain.

-Laz


   
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Narn
 Narn
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Musenfruend I too have for the same increases in both mass and diameter. However, as I've aged I've changed my material, so my pitch has gotten better, and my "sustain" is now twice what it was when I was a teenager. :roll:

TeeHee!

"You want WHAT on the *&%#ing ceiling?" - Michelangelo, 1566


   
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purplefenderstrat
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My head hurts.. :cry:

"im the one who has to die when its time for me to die..so let me live my life, the way i want to.."-Jimi Hendrix-If 6 was 9

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gnease
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If you wonder why I wonder it was just a musing on how string makers come up with their product. If mass is the detirming factor in pitch you could have all of you strings the same size, but varying in mass. If mass has a significant affect could you not then put any string at any location and acheive the correct pitch by use of tension alone? Wouldn't that look funky?

I gotta find something else to think about at work.

If you check out the tensions on the tuned strings (D'Addario and TI list these), you will find they have a fairly symmetrical balance E = e, A = B, D = G. Tensions are slightly higher in the center of the fingerboard (D and G). Why? My guesses:

Well balanced tensions among the strings make them easier to play -- a better, more consistent feel from string to string. Slightly higher tension on the center strings works well, because that's where most players will naturally apply a bit more pressure (better grip, leverage).

A symmetrical profile of tensions will be less likely to cause neck twisting, plus the higher tensioned center strings work directly against the strongest, thickest, truss-barred part of the neck.

Why vary diameter instead of density? It's much easier to change the mass/length this way than find different density materials that actually make good strings.

Don't you have a window at work you can look out?

-Greg

-=tension & release=-


   
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greybeard
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I was talking purely about the characteristics of the string - what a guitar body or bridge does to the vibrations is another matter - the question related to strings.
All other things being equal a string of greater mass will vibrate longer than one of less mass.

I started with nothing - and I've still got most of it left.
Did you know that the word "gullible" is not in any dictionary?
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