everywhere, then we obtain exactly the equation given in Landau and Lifshitz, namely A similar approximation [in the context of equation ], namely , is suggested by Lighthill [see Eq. (7) in the latter paper]. Of course, one might wonder whether we are justified in assuming that . The answer is affirmative, if the flow satisfies certain basic assumptions. In particular, if and , then the assumed relation follows directly from the linear theory of sound waves (see, e.g., the linearized Euler equations and the acoustic wave equation). In fact, the approximate relation between and that we assumed is just a linear approximation to the generic barotropic equation of state of the fluid. However, even after the above deliberations, it is still not clear whether one is justified in using an inherently linear relation to simplify a nonlinear wave equation. Nevertheless, it is a very common practice in nonlinear acoustics as the textbooks on the subject show: e.g., Naugolnykh and Ostrovsky and Hamilton and Morfey. See also Acoustic theory Aeolian harp Computational aeroacoustics References External links M. J. Lighthill, "On Sound Generated Aerodynamically. I. General Theory," Proc. R. Soc. Lond. A 211 (1952) pp. 564–587. This article on JSTOR. M. J. Lighthill, "On Sound Generated Aerodynamically. II. Turbulence as a Source of Sound," Proc. R. Soc. Lond. A 222 (1954) pp. 1–32. This article on JSTOR. L. D. Landau and E. M. Lifshitz, Fluid Mechanics 2ed., Course of Theoretical Physics vol. 6, Butterworth-Heinemann (1987) §75. , Preview from Amazon. K. Naugolnykh and L. Ostrovsky, Nonlinear Wave Processes in Acoustics, Cambridge Texts in Applied Mathematics vol. 9, Cambridge University Press (1998) chap. 1. , Preview from Google. M. F. Hamilton and C. L. Morfey, "Model Equations," Nonlinear Acoustics, eds. M. F. Hamilton and D. T. Blackstock, Academic Press (1998) chap. 3. , Preview from Google. Aeroacoustics at the University of Mississippi Aeroacoustics at the University of Leuven International Journal of Aeroacoustics Examples in Aeroacoustics from NASA Aeroacoustics.info Acoustics Aerodynamics Fluid dynamics Sound