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Subsonic Sound Waves Viewed as a Linear Perturbation in an Inviscid Fluid

In: Comprehensive Applied Mathematical Modeling in the Natural and Engineering Sciences

Author

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  • David J. Wollkind

    (Washington State University, Department of Mathematics)

  • Bonni J. Dichone

    (Gonzaga University, Department of Mathematics)

Abstract

Subsonic sound waves are treated as a linear perturbation to an initially quiescent homogeneous state of a one-dimensional inviscid compressible barotropic fluid of infinite extent. This results in a wave equation satisfied by the density condensation function. The concept of characteristic coordinates relevant to first-order quasi-linear and second-order constant coefficient linear partial differential equations is introduced in a pastoral interlude. Then that method is used to obtain D’Alembert’s solution to the sound wave equation and the physical interpretation of that solution as a traveling wave propagating either to the left or right is discussed. The problems consider two examples giving rise to models involving a first-order linear partial differential equation that are solved by the method of characteristics and a parallel flow situation of a one-dimensional homogeneous inviscid fluid layer the linear normal-mode perturbation analysis of which produces a governing Orr-Sommerfeld ordinary differential equation of motion that is then investigated.

Suggested Citation

  • David J. Wollkind & Bonni J. Dichone, 2017. "Subsonic Sound Waves Viewed as a Linear Perturbation in an Inviscid Fluid," Springer Books, in: Comprehensive Applied Mathematical Modeling in the Natural and Engineering Sciences, chapter 0, pages 251-261, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-73518-4_11
    DOI: 10.1007/978-3-319-73518-4_11
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