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I recently performed an experiment for school which involved plucking different strings on a ukulele at different temperatures and measuring the frequency of sound produced. I expected to find a linear relationship that was shared by all four strings because of the changes in tension of the strings caused by thermal expansion.

However, my data showed that with an increase in temperature,the frequency produced by the thickest string (aka the one with highest linear mass density) decreased. The thinnest string, however, showed a positive linear correlation between temperature and frequency, and the other two strings also seem to follow this trend. In trying to explain these results, I found that the frequency measured is ultimately defined by the ratio of tension to linear mass density of the string (in theory, with an increase in temperature linear mass density would decrease, and the change in tension would be determined by the coefficients of thermal expansion of the strings and the wood of the instrument) but this does not seem to explain the data. Does anyone have some insight?

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  • $\begingroup$ Are all of the strings made of the same material? Not all materials expand when they are heated. Some shrink. $\endgroup$ Aug 17, 2018 at 3:21
  • $\begingroup$ Yes, they are all made of the same nylon fiber $\endgroup$ Aug 17, 2018 at 12:29

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Found this article:

Mechanical Properties of Nylon Harp Strings, by Nicolas Lynch-Aird and Jim Woodhouse

Also I would worry about the wood expansion, the neck bending from one to side to the other given the tension changes. Also the bridge pressure would change?

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  • $\begingroup$ Please don't post links without at least a basic summary of what they contain and how that content answers the question, since link-only answers become useless if the link rots away. Link-only answers aren't considered answers here and may be deleted. It'd be great if you could add some important quotations from link, and possibly give a brief statement of what the link contains and what level of knowledge is needed to understand it. $\endgroup$
    – user191954
    Aug 17, 2018 at 4:37
  • $\begingroup$ Also, the bald google search result-like link looks messy, it's better to include the title of the article and attach a neat link to the pdf itself. $\endgroup$
    – user191954
    Aug 17, 2018 at 4:38
  • $\begingroup$ Thank you for the link; I'm sure it will help to quantify my data a bit. The neck bending is an interesting theory but I don't think it explains my data as one of the strings with the greatest difference was in the middle. $\endgroup$ Aug 17, 2018 at 12:28

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