I Wave damping on a stretched string

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Is there a simple model I can use to describe the damping of a wave on a string? Is c = 2*mu*sqrt(T/mu) where mu is damping coefficient, mu is linear density and T is tension a valid option? I replaced k and m with T and mu from the simple equation found here.

What I am interested in showing is how/if tension affects the damping. My thinking is that seen as changing the tension changes the velocity and therefore wavelength, this will mean that the number of periods will be different compared to at a different applied tension and therefore there will be a difference in loss. Is that thinking correct?
 
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