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Computational Modeling of Stiff Piano Strings Using Digital Waveguides and Finite Differences

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As is well-known, digital waveguides offer a computationally efficient, and physically motivated means of simulating wave propagation in strings. The method is based on sampling the traveling wave solution to the ideal wave equation and linearly filtering this solution to simulate dispersive effects due to stiffness and frequency-dependent loss; such digital filters may terminate the waveguide or be embedded along its length. For strings of high stiffness, however, dispersion filters can be difficult to design and expensive to implement. In this article, we show how high-quality time-domain terminating filters may be derived from given frequency-domain specifications which depend on the model parameters. Particular attention is paid to the problem of phase approximation, which, in the case of high stiffness, is strongly nonlinear. Finally, in the interest of determining the limits of applicability of digital waveguide techniques, we make a comparison with more conventional finite difference schemes, in terms of computational cost and numerical dispersion, for a set of string stiffness parameters.
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Document Type: Research Article

Publication date: 01 March 2005

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  • Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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