This study is aimed to investigate the mechanism of single string beats, which is often observed in stringed instruments, and proposes a vibration model including non-linear effect caused by string stretch. In previous research, beats were expressed even in a single string vibration as well as in plural strings. In recent study, the vibration models including non-linear restoring force were investigated to express the force caused by stretch. To validate the non-linear model, the string vibration was solved by finite-difference time-domain (FD-TD) method using the proposed model, and the results were compared to the string vibration obtained in experiment. In experiment, to observe the effect by string stretch precisely, string was attached on a heavy aluminum board to avoid the influence of mobility at the end-points. Two-dimensional transversal string vibration was measured by optical method using high-speed camera. String parameters related with string stretch were also obtained by measuring the relationship between the displacement and the restoring force of string stretch. From the viewpoint of relationship between initial amplitude and decay curve, numerical simulation and experimental results were compared to each other. The result shows that the beat in string vibration was observed when the string was strongly plucked, while the beat was not observed in weak plucking. By using FD-TD method, simulation results based on plucking condition in experiment show that the beat was observed in case of strong plucking. According to the measurement result and the numerical simulation results, it was considered that the irregular interval beats are derived from difference of resonance frequency in vibration direction and non-linear restoring force caused by string stretch.
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