Vibrational properties of wood along the grain

Abstract

The dynamic Young's modulus (E′_L) and loss tangent (tan δ _L ) along the grain, dynamic shear modulus (G′_L) and loss tangent (tan δ_S) in the vertical section, and density (ρ) of a hundred spruce wood specimens used for the soundboards of musical instruments were determined. The relative acoustic conversion efficiency ($\alpha ,{\text{ }}\sqrt {E'_{\text{L}} /{\kern 1pt} \rho /{\kern 1pt} \tan \delta _{\text{L}} }$) and a ratio reflecting the anisotropy of wood (β, (E′_L/G′_L)(tan δ_S/tan δ_L)) were defined in order to evaluate the acoustic quality of wood along the grain. There was a positive correlation between α and β, and the variation in β was larger than that in α. It seemed logical to evaluate the acoustic quality of spruce wood by a measure of β. By using a cell wall model, those acoustic factors were expressed with the physical properties of the cell wall constituents. This model predicted that the essential requirement for an excellent soundboard is smaller fibril angle of the cell wall, which yields higher α and higher β. On the other hand, the effects of chemical treatments on the α and β of wood were clarified experimentally and analyzed theoretically. It was suggested that the α and β of wood cannot be improved at the same time by chemical treatment.