Index of content:
Volume 118, Issue 3, September 2005
- MUSIC AND MUSICAL INSTRUMENTS 
Simulations of string vibrations with boundary conditions of third kind using the functional transformation method118(2005); http://dx.doi.org/10.1121/1.1992649View Description Hide Description
The functional transformation method (FTM) is an established mathematical method for accurate simulation of multidimensional physical systems from various fields of science, including optics, heat and mass transfer, electrical engineering, and acoustics. It is a frequency-domain method based on the decomposition into eigenvectors and eigenfrequencies of the underlying physical problem. In this article, the FTM is applied to real-time simulations of vibrating strings which are ideally fixed at one end while the fixing at the other end is modeled by a frequency-dependent input impedance. Thus, boundary conditions of third kind are applied to the model at the end fixed with the input impedance. It is shown that accurate and stable simulations are achieved with nearly the same computational cost as with strings ideally fixed at both ends.
118(2005); http://dx.doi.org/10.1121/1.1993127View Description Hide Description
Bensa et al. [J. Acoust. Soc. Am.114, 1095–1107 (2003), Sec. IV] recently proposed a waveguidemodel 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.