Global and local synthetic descriptions of the piano soundboard

TL;DR

This paper models the piano soundboard's acoustic and mechanical behavior, capturing its frequency-dependent properties and radiation patterns with a simplified approach that accounts for structural features like ribs.

Contribution

It introduces a synthetic model of the soundboard's mobility that simplifies complex structural descriptions into a few parameters, improving predictions of sound radiation and structural modifications.

Findings

The soundboard behaves as a homogeneous plate below 1.1 kHz.

Waveguide effects modify the acoustical coincidence phenomenon.

The synthesized mobility matches experimental measurements.

Abstract

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.