Vibrational modes of piano soundboards
Hervé Brelay, Thomas D. Rossing · The Journal of the Acoustical Society of America · 1991
The vibrational modes of the soundboards have been compared in two small upright pianos: one of solid spruce and one of three layers (two thin layers of spruce with a core of poplar). The model frequencies are quite similar, although the mode shapes are somewhat different. In the spruce soundboard, the bending wave velocities for the low-frequency modes appear to increase with the square root of frequency, which suggests that the stiffness of the soundboard plus the ribs is approximately the same along and across the grain (i.e., the soundboard is fully compensated). In the layered soundboard, on the other hand, the nodal lines tend to follow the ribs, indicating that the soundboard is overcompensated. Mode damping does not appear to be substantially different in the two soundboards.