Experimental Evaluation of String Tension Determination Using the Ideal String Model on Kacapi Indung

Abstract

The ideal string vibration model based on Mersenne’s law states that the vibration frequency of a string is determined by its length, linear mass density, and tension. In real musical instruments, string tension is commonly determined from physical parameters under static conditions, although the mechanical behavior of vibrating strings may differ from their equilibrium state. This study aims to evaluate a string tension determination method based on the ideal string vibration model applied to the kacapi indung instrument by comparing static tension and effective dynamic tension estimated from frequency responses obtained through Fast Fourier Transform (FFT) analysis. A quantitative experimental approach was conducted on 18 strings with variations in length, diameter, and material. Static tension was determined using the string deflection method, while effective dynamic tension was calculated from the fundamental frequency obtained from acoustic spectrum analysis. The results show that the effective dynamic tension is systematically lower than the static tension for all observed strings, with relative deviations ranging from 74.39% to 98.20% and an average deviation of 86.69%. These discrepancies indicate that the static approach does not fully represent the mechanical behaviour of strings during oscillation due to non-ideal factors such as damping, harmonic energy redistribution, string stiffness, and mechanical coupling between the strings and the instrument resonator. The findings suggest that the ideal string vibration model remains relevant as an initial theoretical framework; however, its application to real musical instruments requires consideration of more complex dynamic system behaviour. From a physics education perspective, these findings provide an empirical context for demonstrating the validity limits of idealized theoretical models when applied to real acoustic systems.