Numerical simulation of an acoustic tube

  • Jorge Mauricio Ruiz Vera Universidad Nacional de Colombia
  • Leonardo Vásquez Martínez Universidad Nacional de Colombia
Palabras clave: Diferencias finitas, Acústica computacional, Análisis Modal.


In this work, we introduce a staggered finite difference method to analyze and simulate the generation and behavior of sound waves inside a tube. We describe a special numerical treatment on the boundary conditions which model reflection and transmission phenomena by means of the acoustic impedance concept. Through an exhaustive sampling of frequencies and the fast Fourier transform (FFT) a modal analysis is performed when the air inside the tube is subjected to both harmonic and random disturbances. Finally, we analyze the quality factor behavior of the acoustic system to confirm its exponential character as well as its dependence on the acoustic impedance.  The results show the utility of the method in the acoustic phenomena simulation such as reflection, transmission, dissipation of sound waves and resonance in bounded domains. The propose method allows analyzing general cases such as the dispersion of non-harmonic sound waves.


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D. R Bergman, Computational acoustics: theory and implementation. New Jersey, USA: John Wiley & Sons, 2018, 296 p.

M. Kaltenbacher (Ed), Computational Acoustics, Zurich, Switzerland: Springer International Publishing, 2018, 255 p.

I. Riečanová I y A. Handlovičová, “Acoustic Simulations based on FVM Solution of the Helmholtz Equation”, Acta Polytechnica Hungarica Vol 14, no. 5, pp 139 – 150. 2017.

A. Handlovičová, I. Riečanová y N. B. Roozen, “Rigid piston simulations of acoustic space based on Finite volume method”. En: Proceedings of Aplimat, 15-th Conference on Applied Mathematics, Institute of Mathematics and Physics, Faculty of Mechanical Engineering STU, Bratislava, Republica de Eslovaquia, Febrero, 2016, pp. 433-439.

P. Cook, Real Sound Synthesis for Interactive Applications. New York, USA: A K Peters/CRC Press, 2003, 263 p.

A. Kapur, P. Cook, S. Salazar y G. Wang, Programming for Musicians and Digital Artists. New York, USA: Manning Publications Co, 2015, 344 p.

L. D Bartolo, C. Dors y W. J Mansur, “Theory of equivalent staggered grid schemes: application to rotated and standard grids in anisotropic media”, Geophysical Prospecting, Vol 63, no. 5, pp. 1097-1125, Septiembre, 2015. 10.1111/1365-2478.12210

Danggo M. Y., Mungkasi S. A., (2017). A staggered grid finite difference method for solving the elastic wave equations. En: Journal of Physics: Conference Series, Vol 909 (1), pp 1-5

L. Yang, K. S. Mrinal, “Scalar wave Equation Modeling with Time- Space Domain Dispersion-Relation-Based Sttaggered-grid Finite- Difference schemes”, Bulletin of the Seismological Society of America; Vol 101, No 1, pp 141-159, Febrero, 2011.

D.G. Stork y R. E. Berg, The physics of sound. San Francisco, USA: Pearson Education, 2005, 398 p.

K. Morton y D. Mayers, Numerical Solution of Partial Differential Equations. Cambridge, UK: Cambridge University Press, 2005, 278 p.

E. J. Sanchis, “Modelación, simulación y caracterización de materiales acústica de materiales para uso en acústica arquitectónica”, Tesis de Maestría, Universidad Politecnica de Valencia. Valencia, España 2008

A. P. French, Vibraciones y Ondas. Madrid, España: Reverté S.A, 1974,340 p.

L. E. Kinsler, A. B. Coppens, J. V. Sanders y A. R. Frey, Fundamentos de acústica. México, México: Grupo Noriega Editores Limusa, 1992, 592 p.

E. Chu E, Discrete and Continuous Fourier Transforms: Analysis, Applications and Fast Algorithms. London, UK: Chapman and Hall/CRC, 2008, 424 p.

Cómo citar
Ruiz Vera, J. M., & Vásquez Martínez, L. (2019). Numerical simulation of an acoustic tube. Ciencia E Ingeniería Neogranadina, 29(2).