I The effect of temperature on the damping of a guitar string

[SamuuLau]

TL;DR

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.

 

[Baluncore]

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