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Numerical Solution of Sasando String Motion Model
Ari Kusumastuti
1
, Muhammad Khudzaifah
1
, Heni Widayani
1
, and Aminatus Zuhriah
2
1
Department of Mathematics, UIN Maulana Malik Ibrahim Malang
2
Bachelor Degree of Mathematics, UIN Maulana Malik Ibrahim Malang
Jalan Gajayana No.10, Malang, East Java 65144
Keywords: Numerical solution, CTCS, String Motion, Sasando
Abstract: This study describes the problem of string motion on the Sasando musical instrument. This research focuses
on the numerical solution of Sasando string motion model which is a partial differential equation. The
method used to find out the numeric solution is CTCS (Central Time Central Space) method. The explicit
formula of discretization and Von Neuman stability analysis are considered here. The results show the
solution of is stable, which means the movement of the string toward the equilibrium value .
1 INTRODUCTION
Applied mathematics is needed in every part of life
especially to help solve problems related to
mathematical models. Mathematical modeling is a
field of mathematics that seeks to represent and
explain real problems into mathematical equations.
For example, the vibration phenomenon that occurs
along the strings of Sasando can be analyzed by
using mathematical model. The mathematical model
for this problem has been done by Kusumastuti, et
al(Kusumastuti & Brylliant, 2017).
Sasando is one of the traditional musical
instruments originated from Rote Island of Ndao
Regency of East Nusa Tenggara. The distinctive and
beautiful sound makes many people, not only local
people but also the foreign community interested to
examine how this instrument is able to create
beautiful sounds. The problem of string motion on
the Sasando musical instrument is a difficult
problem to analyze directly. Therefore, an effort is
needed to understand the problem, one of which is to
establish a proper measure that can represent the
problem in its real state. In mathematics, this is
known as the mathematical model. The
mathematical model for motion problems in the
Sasando musical instrument is seen as an abstraction
of the strings problem on the complex Sasando
musical instrument presented in the form of a
mathematical language. By modeling the strings on
the Sasando musical instrument, it can be seen the
vibration pattern of the string on the Sasando
instrument in the mathematical equation. Thus, the
understanding of the strings on the Sasando musical
instrument becomes more systematic and easier to
analyze further.
Purwanto, have done research on the analysis
and synthesis of sound signals generated from the
instrument of semi-acoustic guitar. In the study the
strings of the guitar were picked and then the sound
produced was recorded using the SOUND FORGE
program. The recording sound data is then analyzed
by FFT to obtain the sound signal spectrum, and the
components of the composer of the sound signal,
such as fundamental frequency, harmonic
frequency, amplitude, and amplitude ratio. Then the
sound signal construction based on the components
that have been obtained. And the results show that
by adding the damping factor to the sound signal
model make a similar sound with the original sound
from guitar. (Purwanto, et al., 2006)
This study is a follow-up study of previous
research by Kusumastuti, et al who has analyzed the
construction of a strap motion model on a sasando
instrument. In this work, numerical analysis is done
using finite difference method, i.e. Central Time
Central Space (CTCS). Triatmodjo states that finite
difference method is usually used to find the
numerical solution of partial differential equations.
Finite difference schemes approximate the solution
by discretization the partial differential equation.
Kusumastuti, A., Khudzaifah, M., Widayani, H. and Zuhriah, A.
Numerical Solution of Sasando String Motion Model.
DOI: 10.5220/0008525005370541
In Proceedings of the International Conference on Mathematics and Islam (ICMIs 2018), pages 537-541
ISBN: 978-989-758-407-7
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