PEMODELAN FREKUENSI GITAR BASS ELEKTRIK DAN GITAR AKUSTIK DENGAN PENDEKATAN PERSAMAAN DIFERENSIAL PARSIAL ANALITIK = FREQUENCY MODELLING OF ELECTRIC BASS GUITAR AND ACOUSTIC GUITAR USING ANALYTIC PARTIAL DIFFERENTIAL EQUATION APPROACH

Gunawan, Caroline (2023) PEMODELAN FREKUENSI GITAR BASS ELEKTRIK DAN GITAR AKUSTIK DENGAN PENDEKATAN PERSAMAAN DIFERENSIAL PARSIAL ANALITIK = FREQUENCY MODELLING OF ELECTRIC BASS GUITAR AND ACOUSTIC GUITAR USING ANALYTIC PARTIAL DIFFERENTIAL EQUATION APPROACH. Bachelor thesis, Universitas Pelita Harapan.

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Abstract

Banyak kejadian di dalam kehidupan sehari-hari dapat dimodelkan dengan persamaan matematis. Pengerjaan ini disebut sebagai pemodelan matematika. Salah satu kejadian yang digunakan dengan pemodelan adalah frekuensi pada kedua alat musik, yaitu gitar bass elektrik dan gitar akustik. Kedua alat musik tersebut dilakukan pemodelan frekuensi dengan persamaan diferensial parsial (PDP) analitik, dengan langkah penyelesaian pemisahan variabel, mencari solusi nontrivial, kombinasi linier, dan solusi akhir berdasarkan syarat awal PDP tersebut, serta simulasi frekuensi berdasarkan parameter-parameter yang ada dari solusi akhir dan rumus frekuensi. PDP untuk gitar bass elektrik adalah PDP orde 2 homogen. Sementara PDP untuk gitar akustik adalah PDP orde 4 homogen. Hasil dari penelitian ini adalah untuk gitar bass elektrik, semakin tinggi frekuensi pada senar dengan tegangan yang diberikan, semakin rendah massa jenis yang dimiliki oleh senar. Untuk gitar akustik, semakin tinggi frekuensi pada senar dengan tegangan dan Modulus Young yang diberikan, semakin rendah massa jenis dan inersia yang dimiliki oleh senar. Skripsi ini akan memaparkan ilustrasi untuk solusi analitik untuk kedua PDP. / Many situations in the real world can be modelled by mathematical equations. The process is called mathematical modelling. One of the situations that can be modelled is the frequency of musical instruments (electric bass guitar and acoustic guitar). Both musical instruments were frequency modelled with analytic partial differential equation (PDE), with steps of solving PDE with separation of variable, determining nontrivial solution, determining linear combination, and the final solution will be obtained based on the initial condition, with the frequency simulation based on the parameters found from the final solution and frequency formula. PDE for electric bass guitar is non-homogeneous second order. On the other hand, PDE for acoustic guitar is homogeneous fourth order. The result of this research is for the electric bass guitar, the higher the frequency of the string with given tension, the lower the density of the string. Meanwhile for acoustic guitar, the higher frequency of the string with given tension and Young Modulus, the lower density and inertia of the string. This Thesis also present some illustrations of the analytical solutions of both PDEs.

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