The effect of temperature on the damping of a guitar string

In summary, the conversation discusses the effect of temperature on the frequency and damping of a guitar string. The speaker has researched the relationship between temperature and elasticity/tension force but is now questioning how temperature affects the damping of the string. They mention a viscous damping coefficient and express uncertainty about the role of temperature in this coefficient. The conversation also touches on the impact of temperature on other materials in a guitar, such as the neck and wood. The second speaker brings up the drag equation as a potential factor to consider in the relationship between temperature and damping.
  • #1
SamuuLau
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TL;DR Summary
How does temperatue affect damping of a guitar string, assuming temperature doesn't change the other factors, such as the wooden guitar?
I am a high school student and recently I have been working on a project about how temperature affects the frequency of a string emits. I have read blogs like https://www.physicsforums.com/threads/tension-and-frequency-with-change-in-temperature.833185/ and completed the part of thermal expansion to the elasticity/tension force. However, another question that strikes me is how does temperature affect the damping of the string.
I looked up some formulas that might be related, such as the model of $$T\frac{\partial^2 y(x,t)}{\partial x^2} + \beta\frac{\partial y(x,t)}{\partial t}-\rho \frac{\partial^2 y(x,t)}{\partial t^2} = 0$$ Where 𝛽 is a viscous damping coefficient.

I searched about what affects the vicous damping coefficeint and I couldn't find temperature as one of the factors. Am I wrong assuming temperatue changes the damping of a guitar string?

Also, I am assuming the temperature has no effect on any material besides the string such as the guitar neck or wood. I am focusing solely on the metal string.
 
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  • #2
Welcome to PF.

Colder, more dense air, extracts more energy from the string, so it sounds louder initially, but is damped more quickly.
You need to study the drag equation. https://en.wikipedia.org/wiki/Drag_equation
 

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