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

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.