FUNGSI GREEN PADA PERSAMAAN GELOMBANG DAWAI VIBRASI ALAT MUSIK SASANDO GREEN FUNCTION OF THE STRING VIBRATION MODEL ON SASANDO MUSICAL INSTRUMENT

EZRA EFRIZARDI YUSUFA, NIM. 17106010040 (2021) FUNGSI GREEN PADA PERSAMAAN GELOMBANG DAWAI VIBRASI ALAT MUSIK SASANDO GREEN FUNCTION OF THE STRING VIBRATION MODEL ON SASANDO MUSICAL INSTRUMENT. Skripsi thesis, UIN SUNAN KALIJAGA YOGYAKARTA.

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Abstract

Sasando is a musical instrument that is played by picking and originating from Rote Island, East Nusa Tenggara. The sound motion waves on the Sasando musical instrument were modeled by Ari Kusumastuti et al in 2019 in the form of mathematical partial differential equations. Green's function is a formula for finding the fundamental solution of a given partial differential equation and its boundary conditions. This thesis discusses the steps of constructing the Green function from the equation of vibrational string waves in Sasando musical instruments through the expansion of the eigen function and the Laplace transform. The construction of the Green function through the expansion of the eigen function is carried out using the delta dirac function and the Green identity. After the form of the solution for the equation of the vibration string waves on the Sasando musical instrument in which there is a Green function is obtained, then the form of the Green function is obtained through the expansion of the eigen function. The construction of the Green function through the Laplace transform is done by forming a Laplace transform auxiliary equation on the two sides of the vibration string wave equation on a Sasando musical instrument and using the initial conditions. Furthermore, the inverse Laplace transform on the two segments will provide the solution needed by it and forming the Green function on the solution of the vibration string wave equation on the Sasando musical instrument through the Laplace transformation

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