On waveguide modeling of stiff piano strings

Bensa et al. [J. Acoust. Soc. Am. 114, 1095-1107 (2003), Sec. IV] recently proposed a waveguide model for the transverse displacement of a stiff piano string. The study described here is an attempt to cast a complementary light on this topic, based on a common wave approach instead of a modal approach. A pair of weakly attenuated traveling waves and a pair of fast-decaying waves both satisfy the one-dimensional wave equation developed by Bensa et al. These solutions have to be carefully considered, however, for portions of string interacting with the hammer felt, the bridge, or the capo d'astro bar.