Simulations are performed for G string (\(f_1 = \omega_1/2\pi = 196\) Hz)
\(\ell = \) \(0.648\) m \(=\) scale length of Gibson L-5
\(T = 177.1\) N and \(r= 3.3\times 10^{-4}\) m.*
\(E \simeq 198\) GPa.†
These values yield \(B \simeq 1.5\times 10^{-5}\)
\(\Gamma_n = 9.3\times 10^{-4}\) determined by noting that at \(1\) s, string amplitude drops by \(10\) dB, which corresponds to \(\gamma =\ln 10^{1/2} \simeq 1.15\) s\(^{-1}\).
*D'Addario 13-56 medium flatwound chrome strings. Only \(\sim\!\!1/2\) of the string radius consists of the core.
†Polak et al. 2018