@phdthesis{Kappel2012,
  author    = {Kappel, Marcel},
  title     = {Scattering effects in the sound wave propagation of instrument soundboards},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-62676},
  school      = {Universit{\"a}t Potsdam},
  year      = {2012},
  abstract  = {In the western hemisphere, the piano is one of the most important instruments. While its evolution lasted for more than three centuries, and the most important physical aspects have already been investigated, some parts in the characterization of the piano remain not well understood. Considering the pivotal piano soundboard, the effect of ribs mounted on the board exerted on the sound radiation and propagation in particular, is mostly neglected in the literature. The present investigation deals exactly with the sound wave propagation effects that emerge in the presence of an array of equally-distant mounted ribs at a soundboard. Solid-state theory proposes particular eigenmodes and -frequencies for such arrangements, which are comparable to single units in a crystal. Following this 'linear chain model' (LCM), differences in the frequency spectrum are observable as a distinct band structure. Also, the amplitudes of the modes are changed, due to differences of the damping factor. These scattering effects were not only investigated for a well-understood conceptional rectangular soundboard (multichord), but also for a genuine piano resonance board manufactured by the piano maker company 'C. Bechstein Pianofortefabrik'. To obtain the possibility to distinguish between the characterizing spectra both with and without mounted ribs, the typical assembly plan for the Bechstein instrument was specially customized. Spectral similarities and differences between both boards are found in terms of damping and tone. Furthermore, specially prepared minimal-invasive piezoelectric polymer sensors made from polyvinylidene fluoride (PVDF) were used to record solid-state vibrations of the investigated system. The essential calibration and characterization of these polymer sensors was performed by determining the electromechanical conversion, which is represented by the piezoelectric coefficient. Therefore, the robust 'sinusoidally varying external force' method was applied, where a dynamic force perpendicular to the sensor's surface, generates movable charge carriers. Crucial parameters were monitored, with the frequency response function as the most important one for acousticians. Along with conventional condenser microphones, the sound was measured as solid-state vibration as well as airborne wave. On this basis, statements can be made about emergence, propagation, and also the overall radiation of the generated modes of the vibrating system. Ultimately, these results acoustically characterize the entire system.},
  language  = {en}
}