Shock Wave Characteristics in the Initial Transient of an Organ Pipe

Abstract

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.

No enjoyment is transitory; it leaves an impression behind; that impression is abiding, and whatever is done earnestly and industriously imparts even to the mere looker-on a hidden power whose effects spread farther than we can ever know.

Johann Wolfgang von Goethe, Wilhelm Meisters

Apprenticeship, 1795/96, 5. Book, Chapt. X