  Up to around 1.1 kHz, the soundboard of the piano behaves like a homogeneous
plate whereas upper in frequency, it can be described as a set of waveguides
defined by the ribs. In consequence: a) The acoustical coincidence phenomenon
is deeply modified in comparison with that occurring in homogeneous plates
since the dispersion curve of a waveguide can present none, one, or two
coincidence frequencies. This may result in a nonuniformity of the soundboard
radiation in the treble range, corresponding to the so-called killer octave,
where a good sustain is difficult to obtain. b) The mobility (mechanical
admittance) in the direction normal to the soundboard can be synthesised with
only a small number of parameters. It compares well with published measurements
(Giordano, JASA, 1998), in particular the step-like falloff of the local
impedance due to the localisation of the waves between ribs. c) The synthesised
mobility has the same features as those which can be derived independantly,
according to Skudrzyk (JASA, 1980) and Langley (JSV, 1994). This approach
avoids the detailed description of the soundboard, based on a very large number
of parameters. It can be used to predict global changes of the driving point
mobility, and possibly of the sound radiation in the treble range, resulting
from structural modifications.
