Computer simulation of the piano
Isao Nakamura · The Journal of the Acoustical Society of America · 1978
The piano consists of the following mechanisms: (a) transmission of energy from the hammer to the strings, (b) propagation of energy on the strings, (c) transmission of energy from the strings to the soundboard at the bridge, and (d) acoustic radiation by the vibration of the soundboard. These mechanisms are expressed in terms of equivalent electric circuit models, and these models are simulated by computer programs. A half-sinusoidal pulse which is produced by the hammer's stroke, propagates on the special transmission line, and is reflected by the impedances of the bridge end and the fixed end. The transmission and reflection lead to the transformation and decay of the waveform. The driving force at the bridge produces the sound pressure whose waveform is determined according to transmission characteristics of the soundboard. Several waveforms and tones by means of the simulation are presented with the actual waveforms measured. The relations between some constants of the piano and produced tones are discussed.