Shock Wave Characteristics in the Initial Transient of an Organ Pipe

  • Jost Leonhardt FischerEmail author
Part of the Current Research in Systematic Musicology book series (CRSM, volume 5)


A new approach to investigate the role of pressure waves in the initial transient of an organ pipe is presented. By numerical simulations solving the compressible Navier-Stokes equations with suitable boundary and initial conditions, it is possible to retrace the generation, propagation, reflection, damping and radiation of sound waves. The focus is on the contribution of occurring pressure wave fronts in the initial transient that show shock wave characteristics, in particular their role at the formation process of the sound field inside the organ pipe’s resonator. Utilizing spectral analysis as well as extended visualization methods, a wide range of aspects of the dynamics of the initial transient of an organ pipe is discovered. In particular the damping processes in the resonator which are nonlinear are analyzed and discussed in detail. The numerical approach presented in this case study, allows to study the initial transient of an organ pipe with an extraordinary level of precision, thereby helping to understand the underlying first principles of the sound field formation and the mutual interaction of the jet’s flow field and the sound field inside organ pipes and similar wind instruments that produce complex sounds listeners find both interesting and joyful. Animations of the temporal and spatial development of relevant physical quantities like pressure, turbulent kinetic energy, vorticity and velocity magnitude calculated in the numerical simulations are provided as supplementary material.

Supplementary material (1537.6 mb)
Supplementary material 1 (zip 1574534 KB) (1379.2 mb)
Supplementary material 2 (zip 1412251 KB)


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Universität HamburgHamburgGermany

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