Piano Physics at Purdue

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Latest modeling results (2003)



Simple Model of a Piano Soundboard   (N. Giordano) download
The vibrational properties of a simple finite element model of a piano soundboard are considered. Our main focus is on the behavior of the mechanical impedance in the musically important frequency range - 50~104 Hz. The model includes the effects of elastic anisotropy and the ribs. It is argued that the ribs are an essential ingredient for producing the behaviour of the impedance which is observed experimentally. [Journal of the Acoustical Society of America, vol. 102, p. 1159 (1997)]
Sound Production by a Vibrating Piano Soundboard   (N. Giordano) download
The generation of sound by a piano soundboard is investigated experimentally, through measurements of the sound pressure, p, and the soundboard velocity, vb, produced in response to a force applied at the bridge. Results for the ratio p/vb as a function of frequency, for forces applied perpendicular to the soundboard at different locations (i.e., driving points) on the bridge, are presented. At all locations, p/vb is largest at frequencies of order 1 kHz, and falls off below a few hundred Hz and above about 5 kHz. A few results obtained with the force applied along the string direction (i.e., parallel to the plane of the soundboard) are also described. These results are compared and contrasted with previous experiments, and with theoretical expectations. [Journal of the Acoustical Society of America, vol. 104, p. 1648 (1998)]

Plucked Strings and the Harpsichord   (N. Giordano and J. P. Winans II) download
The excitation of a harpsichord string when it is set into motion, i.e., plucked, by a plectrum is studied. We find that the amplitude of the resulting string vibration is approximately independent of the velocity with which the key is depressed. This result is in accord with conventional wisdom, but at odds with a recent theoretical model. A more realistic theoretical treatment of the plucking process is then described, and shown to be consistent with our measurements. The experiments reveal several other interesting aspects of the plectrum-string interaction. [Journal of Sound and Vibration, vol. 224, p. 455 (1999)]

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