Simulation of the sound production mechanism : Acoustical research on the piano Part 2

Abstract

The piano consists of the following mechanisms : (a) transmission of energy from the hammer to the strings, (b) propagation of energy of 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 an equivalent electric circuit model, which is simulated by computer programs. A nearly half-sinusoidal pulse which is produced by the hammer's stroke, propagates on the special transmission line, and is reflected by the impedance of the bridge and the fixed end. The transmission and reflection lead to the transformation and decay of the waveform. The driving velocity of the soundboard is made by supplying the summing forces of the strings at the bridge to the driving point impedance. This velocity produces the sound pressure whose waveform is determined by transmission characteristics of the soundboard. Artificial piano sound is produced from calculated waveforms by a D-A converter. When each fundamental frequency of the group of strings is slightly detuned, beats are produced in each partial which is inharmonic. The changes are slow in the lower partials, but the higher they become, the rapider their changes are. The decay rate of the sound is fast at the prompt sound, but it becomes slowly at the after sound. These are some causes that gives a delicate timbre to the piano.