VIBRATIONS OF PIANO STRINGS AND COUPLING TO THE SOUNDBOARD
AR BAXANDALL, I.D. Brown, CE GOUGH · 2024
In this paper we give a brief account of some measurements of the resonant and transient response of strings on a piano.From such measurements we can derive quantitative information on the strength and nature of the coupling between the vibrating strings and the soundboard at the supporting bridge.This also provides valuable information on the characteristic vibrational response of the soundboard, which must play an important role in determining the tone of a particular instrument, but about which remarkably little infomation appears to have been published.It is well known that sound from a well-tuned piano can persist for very long times after the initial transients have diedaway.Hundley et al [1] argue that this is not caused by a faster decay rate of the upper partials excited but is produced by the slight mistuning of the string doublets and triplets.when a triplet is excited by the hammer in the normal way, all three strings are initially forced to vibrate with equal amplitude.The resulting induced motion of the bridge leads to a decay rate three times faster than that of a single string vibrating alone.These authors argue that the slight mistuning leads to a dephasing of the individual string vibrations.resulting in a decreased force on the bridge and a diminished.but time varying decay rate at long times.weinreich [2 I argues that the problem should be considered self-consistently by describing the vibrations in terms of the normal modes of the string doublets and triplets coupled via their mutual interaction with the soundboard.For a doublet, the modes can be represented as (H) and (H ).where the arrows