String Tension Variation as a Function of Scale Length

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TonyGonzales84

Posts: 78
Joined: Apr. 23 2020
From: San Diego, CA

String Tension Variation as a Functi...

Folks,

In an effort to un-hijack cube_monkey's good question, I am starting this thread to carry on the discussion started in http://www.foroflamenco.com/tm.asp?m=326060&p=1&tmode=1&smode=1

For now this a place holder, and if nothing else, I will report back here, at some frequency, just to not have only radio silence on my part.

Tony

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Tony

REPORT THIS POST AS INAPPROPRIATE | Date Jul. 8 2020 6:04:27

kitarist

Posts: 1715
Joined: Dec. 4 2012

RE: String Tension Variation as a Fu... (in reply to TonyGonzales84)

I can post here the list of papers and dissertations that I found, in case you haven't seen some of them. Maybe as a moving gif/png of title pages; if anything sounds interesting, I can send you the whole paper/dissertation. Stay tuned..

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Konstantin

REPORT THIS POST AS INAPPROPRIATE | Date Jul. 8 2020 6:25:41

TonyGonzales84

Posts: 78
Joined: Apr. 23 2020
From: San Diego, CA

RE: String Tension Variation as a Fu... (in reply to TonyGonzales84)

Thanks, Konstantin -- I'll keep my eyes peeled.

Tony

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Tony

REPORT THIS POST AS INAPPROPRIATE | Date Jul. 8 2020 16:18:39

kitarist

Posts: 1715
Joined: Dec. 4 2012

RE: String Tension Variation as a Fu... (in reply to TonyGonzales84)

Here you go (it's a movie gif):

Images are resized automatically to a maximum width of 800px

Attachment (1)

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Konstantin

REPORT THIS POST AS INAPPROPRIATE | Date Jul. 8 2020 18:39:13

TonyGonzales84

Posts: 78
Joined: Apr. 23 2020
From: San Diego, CA

RE: String Tension Variation as a Fu... (in reply to TonyGonzales84)

Thanks, Konstantin -- I'll see if I can obtain them.

Tony

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Tony

REPORT THIS POST AS INAPPROPRIATE | Date Jul. 8 2020 21:36:00

TonyGonzales84

Posts: 78
Joined: Apr. 23 2020
From: San Diego, CA

RE: String Tension Variation as a Fu... (in reply to TonyGonzales84)

Radio check:

I have skimmed and enjoyed many of Konstantin's referenced articles, and Richard's link to Alan Carruth's article (which now I have referenced and recommended on another Luthierie thread).

I will see what pertinent numerical data I can extract from a couple of the Konstantin articles, specifically, pertaining to vibrating effective masses. I would then have to extract the like equivalent stiffnesses of said masses.

The journey continues.

Tony

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Tony

REPORT THIS POST AS INAPPROPRIATE | Date Jul. 20 2020 23:07:15

TonyGonzales84

Posts: 78
Joined: Apr. 23 2020
From: San Diego, CA

RE: String Tension Variation as a Fu... (in reply to TonyGonzales84)

This is where I bravely tuck my tail and flee! Run awaaaaay!

I am halting my little (unplanned) journey into the world of modern acoustic research. The original question I was looking into was something like, given identical strings tuned to an identical frequency, how does a guitar’s string’s being attached to the flexible and massy guitar top affect the classic, theoretical and idealized tension-length relationship for a string with both ends attached to a rigid support? This relationship is (T2/T1) = (L2/L1)^2 where T is the string’s tension (approximated as constant for each distinct case), and L is its (scale) length (also constant for each distinct case). (T2 and L2 are those of the second guitar, T1 and L1 are of the first guitar.) Not having made progress in answering this question, I recommend continuing using the classic relation.

Solutions, analytical and numeric, very well may exist, knowledge being readily known by the specialists, but I have not been able to find such solutions nor the data that may feed into deriving them. With tongue firmly in cheek, I mention that there could be a hint to why in the deafening silence in the many textbooks on partial differential equations, on wave physics, and on mechanical vibrations that often derive and discuss strings with flexible supports, but with massless springs – not our case! -- No one is showing the string attached to mass-spring systems!

My original attack was to focus exclusively on deriving the fundamental frequency and use a Rayleigh-Ritz type of analysis, to avoid dealing with the full equations of motion. Numeric results along this line of attack would show trends, hopefully allowing understanding of how close our case is to the classical fixed-fixed relation. I might, in the near geologic future (again, tongue firmly planted in cheek), investigate very simple cases similar to the equivalent mass-spring system I assumed in my Rayleigh-Ritz attack…who knows?

Most papers I was able to quickly dig up (including those titles directly provided by Konstantin and Richard – thanks to both!, and the papers I then dug up after reviewing those) result in working in the frequency domain, quantifying and investigating the response of the full guitar when “played.” This work is very interesting, including nonlinear effects of geometry and of materials properties (nylon’s nonlinear elastic behavior, and even the effects due to the winding on the bass strings), not to speak of damping characteristics (again, for investigating response, not for free vibrations – the fundamental frequency problem of our interest).

Many roads coming out of the papers I have found, and of titles provided by Konstantin, lead to ResearchGate, which evidently requires an institutional email address in order to obtain full download privileges. This is a typical and not unreasonable barrier to entry, but one that I need to figure how to get past. I did find my name in there, as a co-author (in a former life) – a potential path to possibly explore later.

I have learned a lot and had fun too!

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Tony

REPORT THIS POST AS INAPPROPRIATE | Date Jul. 21 2020 23:50:37

kitarist

Posts: 1715
Joined: Dec. 4 2012

RE: String Tension Variation as a Fu... (in reply to TonyGonzales84)

Just a quick note that I will follow up in a week or two when I will have access to the papers and an internet connection.

Currently with no internet access to speak of(*); just songbirds, a chipmunk, squirrels, some turtles and frogs, and a lot of canoeing around a small lake.

(*) This post delivered by telegram to Simon who was kind enough to type it up.

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Konstantin

REPORT THIS POST AS INAPPROPRIATE | Date Jul. 22 2020 21:57:24

TonyGonzales84

Posts: 78
Joined: Apr. 23 2020
From: San Diego, CA

RE: String Tension Variation as a Fu... (in reply to TonyGonzales84)

Telegram, Konstantin (and Simon, of course)? That's dedication. I didn't know they still existed. I'm going to wonder now about maybe party-line telephones too. I look forward to an interesting story!

Tony

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Tony

REPORT THIS POST AS INAPPROPRIATE | Date Jul. 23 2020 1:10:09