Research PapersNo Access

A Two-Dimensional Study of Finite Amplitude Sound Waves in a Trumpet Using the Discontinuous Galerkin Method

Janelle Resch

Applied Mathematics, University of Waterloo, Waterloo, ON, Canada N2L 3G1, Canada

Corresponding author.

Search for more papers by this author

Lilia Krivodonova

Applied Mathematics, University of Waterloo, Waterloo, ON, Canada N2L 3G1, Canada

Search for more papers by this author

, and

John Vanderkooy

Physics and Astronomy, University of Waterloo, Waterloo, ON, Canada N2L 3G1, Canada

Search for more papers by this author

https://doi.org/10.1142/S0218396X14500076Cited by:6 (Source: Crossref)

Abstract

A model for nonlinear sound wave propagation for the trumpet is proposed. Experiments have been carried out to measure the sound pressure waveforms of the and notes played forte. We use these pressure measurements at the mouthpiece as an input for the proposed model. The compressible Euler equations are used to incorporate nonlinear wave propagation and compressibility effects. The equations of motion are solved using the discontinuous Galerkin method (DGM) and the suitability of this method is assessed. The third spatial dimension is neglected and the consequences for such an assumption are examined. The numerical experiments demonstrate the validity of this approach. We obtain a good match between experimental and numerical data after the dimensionality of the problem is taken into account.

Keywords:

References

D. T. Blackstock , M. F. Hamilton and A. D. Pierce , Nonlinear Acoustics , eds. M. F. Hamilton and D. T. Blackstock ( Academic , San Diego , 1998 ) . Google Scholar
A. J. Hirschberg et al. , J. Acoust. Soc. Amer. 99 , 1754 ( 1995 ) . Crossref, Web of Science, Google Scholar
P. L. Rendon et al. , J. Acoust. Soc. Amer. 127 , 1096 ( 2009 ) . Crossref, Web of Science, Google Scholar
L. Norman et al. , Acta Acustica united with Acustica 96 , 614 ( 2010 ) . Crossref, Web of Science, Google Scholar
J. Gilbert et al. , ISMA ( 2007 ) . Google Scholar
J. Bachus and T. C. Hundley , J. Acoust. Soc. Amer. 49 , 509 ( 1971 ) . Crossref, Web of Science, Google Scholar
S. J. Elliott and J. M. Bowsher , J. Sound and Vibration 83 , 181 ( 1982 ) . Crossref, Web of Science, Google Scholar
M. B. Lesser and J. A. Lewis , J. Acoust. Soc. Amer. 51 , 1664 ( 1972 ) . Crossref, Web of Science, Google Scholar
M. B. Lesser and J. A. Lewis , J. Acoust. Soc. Amer. 52 , 1406 ( 1972 ) . Crossref, Web of Science, Google Scholar
E. Eisner , J. Acoust. Soc. Amer. 41 , 1126 ( 1967 ) . Crossref, Web of Science, Google Scholar
A. G. Webster , Proc. Nat. Acad. Sci. USA 7 , 275 ( 1919 ) . Crossref, Google Scholar
P. A. Martin , J. Acoust. Soc. Amer. 116 , 1381 ( 2004 ) . Crossref, Web of Science, Google Scholar
V. Pagneux , N. Amir and J. Kergomard , J. Acoust. Soc. Amer. 100 , 2034 ( 1996 ) . Crossref, Web of Science, Google Scholar
J. W. Beauchamp , Analysis of simultaneous mouthpiece and output waveforms of wind instruments , Audio Engineering Society Convention 66 — Audio Engineering Society ( 1980 ) . Google Scholar
B. H. Pandya , G. S. Settles and J. D. Miller , J. Acoust. Soc. Amer. 114 , 3363 ( 2003 ) . Crossref, Web of Science, Google Scholar
M. W. Thompson and J. W. Strong , J. Acoust. Soc. Amer. 110 , 556 ( 2001 ) . Crossref, Web of Science, Google Scholar
J. Gilbert , L. Menguy and M. Campbell , J. Acoust. Soc. Amer. 123 , 1854 ( 2008 ) . Crossref, Web of Science, Google Scholar
J. E. Flaherty et al. , J. Finite Elements in Analysis and Design 38 , 889 ( 2002 ) . Crossref, Web of Science, Google Scholar
A. Richter , J. Stiller and R. Grundmann , J. Comp. Acoust. 15 , 123 ( 2007 ) . Link, Web of Science, Google Scholar
A. H. Benade , Fundamentals of Musical Acoustics ( Dover Publications , New York , 1900 ) . Google Scholar
N. H. Fletcher , Rep. Prog. Phys. 62 , 723 ( 1998 ) . Crossref, Web of Science, Google Scholar
R. Feynman , The Feynman Lectures on Physics ( Addison-Wesley , California , 1990 ) . Google Scholar
A. Richter , J. Fluids Eng. 134 , 041104 ( 2012 ) . Crossref, Web of Science, Google Scholar
B. Cockburn and C. W. Shu , J. Comp. Phys. 141 , 119 ( 1998 ) . Crossref, Web of Science, Google Scholar
L. Krivodonova and M. Berger , J. Comp. Phys. 38 , 492 ( 2002 ) . Google Scholar
N. H. Fletcher and T. D. Rossing , The Physics of Musical Instruments ( Springer-Verlag , New York , 1991 ) . Crossref, Google Scholar
W. Kausel and T. Moore, Universitat fur Musik und darstellende Kunst Weiin (2010) pp. 1–46. Google Scholar