How to calculate the damping factor for a vibrating string?

[deadstar33]

I'm running a finite element simulation of a vibrating guitar string, but I do not know how to calculate the correct damping factor for the string as it oscillates in air. I don't have information regarding how many times it will oscillate before the oscillation damps out, but I do have all the physical characteristics of the string. It has a young's modulus of 205 GPa, a Poisson's ratio of 0.31, the working length of the string is 0.648m, the mass of the string is 8.445 x 10^-4 kg, the density of the string is 8890kg/m^3, and it has a radius of 0.2159 x 10^-3 m. I converted everything into S.I units for convenience in the calculations.

Using this data, is there any way to calculate the damping coefficient between the string and air? I've done research but all the methods I've seen of calculating this require values that I don't have, such as the damping coefficient, c. Also, it requires the stiffness of the string, k. Are Young's modulus (E) and stiffness (k) the same thing? Am I correct in saying they are the inverse of each other? As in, 1/E = k?

Thanks.

Edit: My mistake, it's k = AE/L. So I have now applied this formula and calculated the stiffness to be 46.3269 x 10^3 N/m. Using this, I have calculated the critical damping coefficient using the formula Cc = 2(km)^1/2, so that Cc = 12.5097. Now I just need to calculate the damping coefficient, c. Am I using the right method?

 

[Henryk]

No, you don't have enough information to calculate the damping coefficient. The natural frequencies of a string depend on the tension and the mass per unit length (ok, in ideal case). The tension is adjustable (that's how you tune the guitar). Damping of string oscillations is the result of two processes: emission of sound waves (that take the energy out of the string) and friction (which converts energy into heat). The friction is just viscosity of the string but presume the viscosity of the guitar body would also play a role. There is no published data that would let you calculate the damping coefficient (at one point I was looking for that, didn't find anything).

 

[Couchyam]

Here's my advice:
(i) Model the local viscous dissipation of the string using two-dimensional Stokesian (non-inertial) flow around a disk.
(ii) If you have one, estimate the total acoustic dissipation from a dB-reader placed near the string (where cylindrical symmetry is strongest.)
Compare the two estimates.