Piano string excitation IV: The question of missing modes
Donald Elliott Hall, Peter J. Clark · The Journal of the Acoustical Society of America · 1987
It is usually said that a force applied to an extended vibratory system is incapable of exciting any normal mode that has a node at that point. Thus piano hammers positioned to strike the strings at certain fractions of their length should produce spectra with ‘‘missing modes.’’ However, this has been disputed by some observers, and it is sometimes suggested that more careful theoretical treatments would justify a restoration of those modes. Spectra of string motion have been measured as a function of hammer position by moving a piano action frame in small increments along the bed of the case. It is found that there are indeed sharp minima in mode amplitudes (on the order of 20 to 30 dB down) as the striking point passes within a few millimeters of the nodal positions. Possible limitations on the theoretical arguments are discussed, and it is concluded that the small residual strengths in the nearly missing modes can be well accounted for by finite soundboard admittance.