Sound Propagation: An Impedance Based Approach

Acknowledgments.

1 Vibration and Waves.

1.1 Introduction/Study Objectives.

1.2 From String Vibration to Wave.

1.3 One-dimensional Wave Equation.

1.4 Specific Impedance (Reflection and Transmission).

1.5 The Governing Equation of a String.

1.6 Forced Response of a String: Driving Point Impedance.

1.7 Wave Energy Propagation along a String.

1.8 Chapter Summary.

1.9 Essentials of Vibration and Waves.

1.9.1 Single- and Two-degree of Freedom Vibration Systems.

1.9.2 Fourier Series and Fourier Integral.

1.9.3 Wave Phenomena of Bar, Beam, Membrane, and Plate.

Exercises.

2 Acoustic Wave Equation and Its Basic Physical Measures.

2.1 Introduction/Study Objectives.

2.2 One-dimensional Acoustic Wave Equation.

2.3 Acoustic Intensity and Energy.

2.4 The Units of Sound.

2.5 Analysis Methods of Linear Acoustic Wave Equation.

2.6 Solutions of the Wave Equation.

2.7 Chapter Summary.

2.8 Essentials of Wave Equations and Basic Physical Measures.

2.8.1 Three-dimensional Acoustic Wave Equation.

2.8.2 Velocity Potential Function.

2.8.3 Complex Intensity.

2.8.4 Singular Sources.

Exercises.

3 Waves on a Flat Surface of Discontinuity.

3.1 Introduction/Study Objectives.

3.2 Normal Incidence on a Flat Surface of Discontinuity.

3.3 The Mass Law (Reflection and Transmission due to a Limp Wall).

3.4 Transmission Loss at a Partition.

3.5 Oblique Incidence (Snell’s Law).

3.6 Transmission and Reflection of an Infinite Plate.

3.7 The Reflection and Transmission of a Finite Structure.

3.8 Chapter Summary.

3.9 Essentials of Sound Waves on a Flat Surface of Discontinuity.

3.9.1 Locally Reacting Surface.

3.9.2 Transmission Loss by a Partition.

3.9.3 Transmission and Reflection in Layers.

3.9.4 Snell's Law When the Incidence Angle is Larger than the Critical Angle.

3.9.5 Transmission Coefficient of a Finite Plate.

Exercises.

4 Radiation, Scattering, and Diffraction.

4.1 Introduction/Study Objectives.

4.2 Radiation of a Breathing Sphere and a Trembling Sphere.

4.3 Radiation from a Baffled Piston.

4.4 Radiation from a Finite Vibrating Plate.

4.5 Diffraction and Scattering.

4.6 Chapter Summary.

4.7 Essentials of Radiation, Scattering, and Diffraction.

4.7.1 Definitions of Physical Quantities Representing Directivity.

4.7.2 The Radiated Sound Field from an Infinitely Baffled Circular Piston.

4.7.3 Sound Field at an Arbitrary Position Radiated by an Infinitely Baffled Circular Piston.

4.7.4 Understanding Radiation, Scattering, and Diffraction Using the Kirchhoff–Helmholtz Integral Equation.

4.7.5 Scattered Sound Field Using the Rayleigh Integral Equation.

4.7.6 Theoretical Approach to Diffraction Phenomenon.

Exercises.

5 Acoustics in a Closed Space.

5.1 Introduction/Study Objectives.

5.2 Acoustic Characteristics of a Closed Space.

5.3 Theory for Acoustically Large Space (Sabine's theory).

5.4 Direct and Reverberant Field.

5.5 Analysis Methods for a Closed Space.

5.6 Characteristics of Sound in a Small Space.

5.7 Duct Acoustics.

5.8 Chapter Summary.

5.9 Essentials of Acoustics in a Closed Space.

5.9.1 Methods for Measuring Absorption Coefficient.

5.9.2 Various Reverberation Time Prediction Formulae.

5.9.3 Sound Pressure Distribution in Closed 3D Space Using Mode Function.

5.9.4 Analytic Solution of 1D Cavity Interior Field with Any Boundary Condition.

5.9.5 Helmholtz Resonator Array Panels.

Exercises.

Index.