# Guitar String Maximum Travel Distance

• Dejoblue
In summary: However, I am curious as to how I could calculate the maximum distance, crest, and string thickness at the center of the string to avoid fret buzz. In summary, to avoid fret buzz, the string must be at a certain height on the fretboard, and the thickness of the string must be consistent throughout the length of the string.
Dejoblue
I would like to calculate the maximum distance, crest, a guitar string will travel at it's center when plucked in order to determine how high the string needs to be on the fretboard to avoid striking parallel frets and thus avoiding "fret buzz".

Example:

0.762 mm string thickness with 6.35029 kg of tension to get A=440 Hz @ 647.7 mm string length
where a force Z provides 5 mm of string movement @ point 161.925 mm from one end of the string length and vertical movement Y occurs.

X = string length
Y = movement I am interested in
Z = initial force stroke

I need to solve for the initial force required to move the string under tension at the specific place, 1/4 of the length, and then I think I can use sinusoidal formulas? It is actually circular, since the lateral movement Z causes a vertical movement Y. What formulas should I use?

I plan to post the results I calculate for all strings of a 6 - 8 string guitars at different intervals and different initial conditions(IE frequencies, thicknesses, scale lengths, etc.) on my blog.

http://dejablueguitar.blogspot.com

Scroll down to see my balanced string tension article and calculations. I wish to do something similar for string travel at the crest for many strings etc.

Thank you in advance for any help.

PS: guitarists do not actually stroke laterally they stroke across and down at the same time, as well as up with upstrokes, and the movement is actually more elliptical. Dunno if this matters or if the equations bear that out regardless. I am interested in looking at these initial conditions with an ideal perfectly lateral stroke to see if the results are even feasible, IE if the crest radius is more than 3 mm under "ideal" conditions then it is not really relevant.

If you model a guitar string as a perfect classical string, then the standing modes (the natural harmonics of the string) can be excited with any arbitrarily small initial displacement. In other words, there is no lower bound on the force required to pluck a string and get it ringing very softly.

Of course a guitar string is not a perfect string and there are other effects going on, but the ideal string approximation would be a good approximation for the guitar string at very small displacements of the string (very light plucks, and thus very soft notes). So the minimum amplitude of the harmonics is not really relevant for calculating how high your strings should sit above the frets.

Really the best way to determine fret height is by seeing whether you get clatter when the guitar is being played loudly (or as loud as the player would like to be able to play). Of course if you really yank vertically on the guitar string, even if it is at the right height to ordinarily avoid clatter, then a strong enough yank will cause the string to hit the fret. Also if the player of the guitar has a very horizontal picking style, they may be able to play very loudly without any interference with the frets--the strings can (in principle) just move around in the plane parallel with the plane of the frets. All these things could happen regardless of whatever (reasonable) initial fret heights and string tensions you want. It all comes down to what the player's style is and what they would like to be able to do. (In fact many "slap bass" bass guitarists do indeed really yank on the strings--they call it "popping"--to get them to hit against a fret. e.g. )

Calculating these things from basic physical principles is a mammoth task and you would be better off just being a little more "empirical" with how you try to configure a guitar. People who work on guitars have all sorts of rules of thumb for configuring the fret height--setting your bridge height/tremolo tension, adjusting the truss rod, setting the bridge saddles, even your tuning and the kind of strings you use--all come into play in many ways that would be quite difficult to calculate.

Last edited by a moderator:
I appreciate your help and source references.

This is on electric guitar using a plectrum. I used a ruler to measure at what point I could hear the string go out of tune from being struck, this was at 5 mm on the A string and a very hard stroke. More likely I would be using 2 - 3 mm strokes. This 5 mm stroke is far beyond what will cause "fret buzz". My current "action"(string distance from the fretboard) is 2 mm at the 12th fret, ostensibly 1/2 the length of the string.

Perhaps I should have prefaced and or elaborated on my question.

I have played guitar for 24 years and have serviced my own instruments as long. I understand completely these "rules of thumb" and can cite many of the sources I have used over the years as well as my personal preferences.

I understand that neck relief is a necessity(of preference) to counteract the elliptical motion of the strings along it's length.

I also understand that this initial endeavor does not entail actual fretting.

I understand that a harder stroke WILL cause buzz.

Nut and bridge height will be determined by the crest of the string's movement.

i also realize that the crest may travel along the length of the string, I am interested in it's greatest point.

I also realize that this is a "monumental" task, but it is something I am very interested in performing. Furthermore it becomes even more monumental when I next calculate the crest distance 1" away from the nut, as it will be a smaller movement but it what actually causes the "fret buzz".

At any rate, for the current calculations let us assume a perfect lateral stroke of 5mm. I need to calculate the force needed to move a string 5mm under tension at a point that is 1/4 the length of the string away from one side.

Let us also assume no fretboard is involved, just the simple distance traveled at the crest of the ellipse.

Then I also need to calculate the crest once the string is released from that initial 5 mm starting point.

Please be aware I am not asking for anyone to do numerous calculations, if one can simply point me to a formula I am wanting to do this myself or better yet give one example calculation.

I do appreciate requesting and providing clarification. I also intend to participate in discussion here to assess what is relevant to my application as well as the potential for other applications.

Last edited:
Ahh i think i understand now. The initial force is arbitrary so the amplitude will vary. Doh. Hmm. Well maybe we can figure out what it would be with a maximum of 5 mm.

Would I just use the wave equation?

## 1. What is guitar string maximum travel distance?

Guitar string maximum travel distance refers to the maximum distance that a guitar string can move when plucked or strummed. This distance is usually measured in millimeters or inches and varies depending on the type and thickness of the string.

## 2. Why is guitar string maximum travel distance important?

This measurement is important because it affects the sound and playability of the guitar. If the maximum travel distance is too short, the string may feel stiff and produce a muted sound. On the other hand, if it is too long, the string may feel loose and produce a buzzing sound.

## 3. How is guitar string maximum travel distance measured?

The maximum travel distance is measured by plucking the string and measuring the distance it moves from its resting position to its maximum displacement. This can be done using a ruler or other measuring device. It is important to note that the measurement may vary depending on the tension and tuning of the string.

## 4. What factors affect guitar string maximum travel distance?

The main factors that affect maximum travel distance are the tension and thickness of the string. Thicker strings tend to have a shorter maximum travel distance due to their higher tension, while thinner strings have a longer maximum travel distance. Additionally, the type of string (e.g. steel, nylon) and the guitar's setup (e.g. action height, neck relief) can also affect the maximum travel distance.

## 5. How can I adjust the guitar string maximum travel distance?

The maximum travel distance can be adjusted by changing the tension in the string. This can be done by adjusting the tuning pegs or using a capo. It is also possible to adjust the string's action height or neck relief to indirectly affect the maximum travel distance. However, it is important to make these adjustments carefully, as they can also affect other aspects of the guitar's playability and sound.

• Classical Physics
Replies
1
Views
684
• Introductory Physics Homework Help
Replies
5
Views
806
• Classical Physics
Replies
1
Views
2K
• Introductory Physics Homework Help
Replies
7
Views
1K
• Mechanics
Replies
34
Views
2K
• Special and General Relativity
Replies
75
Views
3K
• Introductory Physics Homework Help
Replies
4
Views
1K
• Introductory Physics Homework Help
Replies
6
Views
890
• Mechanical Engineering
Replies
37
Views
15K
• Introductory Physics Homework Help
Replies
2
Views
5K