The vibration of a struck string / A coustical research on the piano,Part 1
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概要
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Vibrations of piano strings struck with an elastic hammer are studied by using equivalentcircuit models based on the impedance analogy and the mobility analogy respectively. When the tension of a piano string alone is considered, neglecting its elasticity, the string and hammer system has an analogy with an electric transmission line, the hammer being represented by an inductance and a capacitance. An analogue simulator based on the models was designed and used for the study of the string and hammer system. Various waveformes, contact times, and the maximum contact force in each case were obtained by using the simulator. The reason for the appearance of even harmonics series in a high frequency region of piano keys, clearly shown in the simulator, is explained;and the method of their adjustment is suggested. A velocity waveform is determined by the resultant of two vertical tension waveforms in the simulators. The characteristics of these waveforms are shown compared with those from an actual piano. The contact forces, from which their vertical tensions can be reduced, are calculated from the equivalent circuits. Waveforms in all the cases become very similar to damped half sinusoidal waves. The energy transmission from a hammer to a string, including its efficiency at a low-frequency region, is discussed.
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