Analytical solution of the string vibration model on Sasando musical instrument

Kusumastuti, Ari, Jamhuri, Mohammad and Hidayati, N. A. (2019) Analytical solution of the string vibration model on Sasando musical instrument. Presented at Journal of Physics: Conference Series, 10th of November 2019, Indonesia.

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Abstract

This research constructs mathematic model for string vibration on Sasando that expressed as a second-order linear partial differential equation with u denote the vertical displacement experienced by the string at the point x at time t. Besides, the purpose of this research is to determine analytical solution using a method known as separation of variable. There are three analytical solutions from three cases based on constant coefficient values. Case 1 occurs when . Based on he simulation, the string produces a quarter wave within 3 seconds. This means the vibration wavelength 0.083 Hz. In this case the vertical displacement of the string is back to quiescent after vibrating to produce a quarter wave. Case 2 occurs when . The string produces 3.5 waves within 3 seconds, means the vibration wavelength is 1.67 Hz. In this case, the farthest vertical displacement (amplitude) become smaller drastically and back to quiescent. Case 3 occurs when . The vibration wavelength of the string is 2.83 Hz, with 7.5 waves within 3 seconds. The vertical displacement decreases periodically and back to quiescent at a certain time. Analysis of 2-dimensional graph for vertical displacement u(x,t) is done with n = 1,2,3,4,5 which is compared with profile of u(x,t) Gulla (2011). Based on results of the model were mentioned before, the mathematical model of string vibration on Sasando has the similar profile as Gulla (2011). For further, this research is suggested to perform a graph profile analysis of other cases that may arise with variation of parameter values.

Item Type:	Conference (Paper)
Keywords:	sasando; musical instrument
Subjects:	01 MATHEMATICAL SCIENCES > 0102 Applied Mathematics
Divisions:	Faculty of Mathematics and Sciences > Department of Mathematics
Depositing User:	Ari Kusumastuti
Date Deposited:	14 Apr 2023 14:59

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