Vibrational and acoustical characteristics of the piano soundboard

TL;DR

This study investigates the vibrational and acoustical properties of an upright piano soundboard, revealing its linear response, modal behavior, and waveguide effects, which influence sound radiation especially in the treble range.

Contribution

It introduces a high resolution modal analysis technique and provides a detailed characterization of the soundboard's vibrational modes and waveguide behavior across frequencies.

Findings

Modal density varies between 0.05 and 0.01 modes/Hz.

Mean loss factor is approximately 2%.

Soundboard behaves as a set of waveguides above 1.1 kHz.

Abstract

The vibrations of the soundboard of an upright piano in playing condition are investigated. It is first shown that the linear part of the response is at least 50 dB above its nonlinear component at normal levels of vibration. Given this essentially linear response, a modal identification is performed in the mid-frequency domain [300-2500] Hz by means of a novel high resolution modal analysis technique (Ege, Boutillon and David, JSV, 2009). The modal density of the spruce board varies between 0.05 and 0.01 modes/Hz and the mean loss factor is found to be approximately 2%. Below 1.1 kHz, the modal density is very close to that of a homogeneous isotropic plate with clamped boundary conditions. Higher in frequency, the soundboard behaves as a set of waveguides defined by the ribs. A numerical determination of the modal shapes by a finite-element method confirms that the waves are localised between the ribs. The dispersion law in the plate above 1.1 kHz is derived from a simple waveguide model. We present how the acoustical coincidence scheme is modified in comparison with that of thin plates. The consequences in terms of radiation of the soundboard in the treble range of the instrument are also discussed.