Freq change- string under const tension

[Beaubello]

Given a nylon guitar(e.g.) string stretched across 2 boundary nodes, a makeshift "nut" and "bridge" on a workbench. At the bridge end the string is tied to an overhanging weight in order to maintain const tension ( unlike a string instrument where the pegs are free to turn gradually and permit a change in tension with attendant detuning ). How would the frequency change as a function of temperature and humidity ( in say 20 - 80 deg F )? Would frequency change be due to any significant extent to a change in string mass/L, largely a result of the varying speed of sound in air or to some other cause? Similarly how should strings of other various materials compare with respect to their frequency stabilities?
Finally with regard to string instrument application might such an investigation have practical implications for choice of string material to better hold tuning or is string detuning the overwhelming result of the change in string tension from turning pegs?

 

[matthewgill]

The string tension is not lost via the tuning pegs, unless they are of very very low quality. On a guitar for example, they can be locking. It is common that the wood of the instrument expands/contracts with temperature... pulling the strings with it. Sometimes when strings get old they don’t hold there pitch quite so well, but this would be the strings' fault not the tuning pegs', something to experiment with there?

 

[astrokreng]

I would first like to clarify that frequency change in a string under constant tension is a complex phenomenon influenced by various factors such as temperature, humidity, string material, and string length. To accurately predict the frequency change, a detailed analysis and experiment would be required.

Regarding the specific scenario described, the frequency change of the nylon guitar string would primarily be affected by the change in tension due to temperature and humidity. As the temperature increases, the string would expand, causing a decrease in tension and a decrease in frequency. On the other hand, an increase in humidity would cause the string to absorb moisture and become heavier, leading to an increase in tension and frequency. However, the specific extent of frequency change would depend on the material properties of the string and the weight used to maintain constant tension.

The change in string mass/length would also play a role in the frequency change, as it affects the speed of sound in the string. A change in temperature and humidity can alter the string's mass and density, leading to a change in the speed of sound and consequently, the frequency. However, the impact of this factor would depend on the specific material used for the string.

In terms of comparing strings of different materials, it is difficult to make a general statement about their frequency stabilities. While some materials may be more affected by temperature and humidity, others may be more stable. Therefore, a detailed investigation would be required to compare the frequency stabilities of strings made from different materials.

In terms of practical implications for string instrument application, this investigation could provide valuable insights into choosing the right string material to maintain tuning stability. However, it is essential to note that string detuning can also be influenced by factors such as the quality of the instrument, the skill of the musician in tuning, and the type of pegs used. Therefore, a comprehensive analysis would be required to determine the relative importance of each factor in string detuning.

In conclusion, the frequency change in a string under constant tension is a complex phenomenon influenced by multiple factors. An investigation into the effects of temperature and humidity on string frequency would require a detailed analysis and experiment to accurately predict and compare the frequency stabilities of strings made from different materials.