PEMODELAN FREKUENSI DAN SIMULASI GETARAN SENAR GITAR BASS LISTRIK DAN GITAR AKUSTIK [FREQUENCY MODELING AND VIBRATION SIMULATION OF ELECTRIC BASS AND ACOUSTIC GUITAR STRINGS]

Caroline Gunawan, Helena Margaretha, Lina Cahyadi, Petrus Widjaja

Abstract


Mathematical equations can represent numerous real-world scenarios, a process known as mathematical modelling. Within this paper, we undertake modelling two musical instruments, specifically the electric bass guitar and the acoustic guitar. Our approach uses partial differential equations (PDEs) to represent these instruments accurately. By establishing the initial condition, we derive the final solution and simulate the frequency using parameters obtained from this solution alongside a frequency formula. The PDE for the electric bass guitar is of non-homogeneous second order, while the PDE for the acoustic guitar is of homogeneous fourth order. The simulation outcomes demonstrate that a lower vibration frequency for the electric bass guitar corresponds to a decreased string density, given a fixed tension. Similarly, this correlation holds for the acoustic guitar. With fixed string tension and Young's Modulus, a lower string density leads to a higher frequency and reduced inertia. Additionally, we provide graphical representations of the analytical solutions for both PDEs. 


Bahasa Indonesia Abstract:

Persamaan matematika dapat memodelkan banyak situasi dalam dunia nyata. Proses ini disebut pemodelan matematika. Salah satu contoh yang dapat dimodelkan adalah frekuensi alat musik (gitar bass listrik dan gitar akustik). Kedua alat musik tersebut dimodelkan frekuensinya dengan persamaan diferensial parsial (PDP). Solusi akhir akan diperoleh berdasarkan kondisi awal. Simulasi frekuensi dilakukan berdasarkan parameter yang ditemukan dari solusi akhir dan rumus frekuensi. PDP untuk gitar bass listrik adalah orde dua non-homogen, dan PDP untuk gitar akustik adalah orde empat homogen. Hasil simulasi menunjukkan bahwa untuk gitar bass dengan tegangan tertentu, senar dengan densitas rendah menghasilkan frekuensi getaran yang lebih rendah. Hasil yang konsisten juga ditunjukkan untuk gitar akustik. Pada tegangan senar dan Modulus Young yang diberikan, senar dengan densitas rendah menghasilkan frekuensi yang lebih tinggi dan inersia yang lebih rendah. Beberapa grafik solusi analitik dari kedua PDP tersebut juga ditampilkan dalam artikel ini.


Keywords


acoustic guitar; electric bass guitar; frequency simulation; partial differential equation



DOI: http://dx.doi.org/10.19166/jstfast.v7i2.7594

Full Text:

PDF

References


Anton, H., & Rorres, C. (2005). Elementary linear algebra (9th ed.). John Wiley & Sons, Inc.

Arfken, G. B., Weber, H. J., & Harris, F. E. (2013). Mathematical methods for physicists (7th ed.). Elsevier, Inc.

Brown, J. W., & Churchill, R. V. (2009). Complex variables and applications (8th ed.). McGraw-Hill Companies.

Harmonic Motion. (N.d.) Retrieved July 12, 2022 from https://labs.phys.utk.edu/mbreinig/phys221core/modules/m11/harmonic_motion.html

Kobayashi, T., Wakatsuki, N., & Mizutani, K. (2010). Inharmonicity of guitar string vibration influenced by body resonance and fingering position. Proceedings of the International Symposium on Music Acoustics (1321). Associated Meeting of the International Congress on Acoustics.

Kusumastuti, A., Jamhuri, M., & Hidayati, N. A. (2019). Analytical solution of the string vibration model on Sasando musical instrument. Journal of Physics: Conference Series, 1321, 022088. http://doi.org//10.1088/1742-6596/1321/2/022088

Lambson, O. C. (2018). The effects of a magnetic pickup on the vibration response of an electric guitar string [Thesis]. Stellenbosch University, Afrika.

Strauss, W. A. (2008). Partial differential equations: An introduction (2nd ed.). John Wiley & Sons, Ltd.

Vinod Kumar, A. S., & Ganguli, R. (2011). Violin string shape functions for finite element analysis of rotating Timoshenko beams. Finite Elements in Analysis and Design, 47(9):1091-1103. https://doi.org/10.1016/j.finel.2011.04.002

Wijnand, M., d’Andréa-Novel, B., Helie, T., & Roze D. (2020). Active control of the axisymmetric vibration modes of a tom-tom drum using a modal-based observer-regulator. Forum Acusticum (pp. 639–646). HAL Open Science. http://doi.org/10.48465/fa.2020.0439


Refbacks

  • There are currently no refbacks.


Copyright (c) 2023 Caroline Gunawan, Helena Margaretha, Lina Cahyadi, Petrus Widjaja

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

favicon Faculty of Science and Technology | Universitas Pelita Harapan | Lippo Karawaci, Tangerang, Indonesia, 15811 | Tel +62 21 5466057 | Fax +62 21 5461055