Modeling of angklung to determine its pitch frequency

Abstract

The angklung is an Indonesian traditional musical instrument made entirely of bamboo. It usually consists of two or three rattle tubes that generate sound by vibrating the tubes. The generated sound is resonated by a rattle resonance tube to make it louder. The rattle tube is carved in a traditional way from a piece of bamboo with a certain length and diameter that are passed from generation to generation to produce the desired tone. In this investigation, we develop a mathematical model of sound generation by a rattle tube and formulate an equation for the frequency of the vibrated rattle tube from its physical and geometrical parameters. Since the rattle tube is not perfectly cylindrical, the frequency of the vibrated rattle tube is derived from the frequency equation for a perfectly cylindrical tube with a modification of the geometrical parameters to make them appropriate for the shape of the rattle tube. This equation can determine the tone frequency for given geometrical parameters of the tube and explain the relationship between the generated tone frequency and the resonant frequency. The model also shows that the discrepancy between the calculated and generated frequencies of the rattle tube is within the response of human ears.