Aeroacústica

An Introduction to Acoustics
S.W. Rienstra & A. Hirschberg Eindhoven University of Technology 10 November 2012

This is an extended and revised edition of IWDE 92-06. Comments and corrections are gratefully accepted.

This file may be used and printed, but for personal or educational purposes only. c S.W. Rienstra & A. Hirschberg 2004.

Contents
Preface 1 1.1 1.2 2 2.1 2.2 Some fluid dynamics Conservation laws and constitutive equations . . . . . . . . . . . . . . . . . . . . . Approximations and alternative forms of the conservation laws for ideal fluids . . . . . Wave equation, speed of sound, and acoustic energy Order of magnitude estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wave equation for a uniform stagnant fluid and compactness 1 1 4 8 8 . . . . . . . . . . . . . 11

2.2.1 Linearization and wave equation . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2.2 Simple solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2.3 Compactness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3 Speed of sound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3.1 Ideal gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3.2 Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.3.3 Bubbly liquid at low frequencies . . . . . . . . . . . . . . . . . . . . . . . . 16 2.4 2.5 2.6 Influence of temperature gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Influence of mean flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Sources of sound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.6.1 Inverse problem and uniqueness of sources . . . . . . . . . . . . . . . . . . . 19 2.6.2 Mass and momentum injection . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.6.3 Lighthill’s analogy . . . . . . . . . . . . . . . . . . . . . . . . . . . .