UNDERSTANDING ACOUSTICS : an experimentalists view of sound and vibration.

The Acoustical Society of America
Preface to the Second Edition
Preface to the First Edition
List of Recurring Symbols
	Roman Lower Case
Roman Lower Case
	Roman Upper Case
	Greek Lower Case
	Greek Upper Case
	Subscripted Upper-Case Roman
	Subscripted Lower-Case Roman
	Subscripted Lower-Case Greek
	Phasors
	Other
Acknowledgments
Contents
About the Book
About the Author
Chapter 1: Comfort for the Computationally Crippled
	1.1 The Five Most Useful Math Techniques
		1.1.1 Taylor Series
		1.1.2 The Product Rule or Integration by Parts
		1.1.3 Logarithmic Differentiation
	1.2 Equilibrium, Stability, and Hooke´s Law
		1.2.1 Potentials and Forces
		1.2.2 A Simple Pendulum
	1.3 The Concept of Linearity
	1.4 Superposition and Fourier Synthesis
	1.5 Convenience (Complex) Numbers
		1.5.1 Geometrical Interpretation on the Argand Plane
		1.5.2 Phasor Notation
		1.5.3 Algebraic Operations with Complex Numbers
		1.5.4 Integration and Differentiation of Complex Exponentials
		1.5.5 Time Averages of Complex Products (Power)
	1.6 Standard (SI) Units and Dimensional Homogeneity
	1.7 Similitude and the Buckingham Pi-Theorem (Natural Units)
		1.7.1 Three Simple Examples
		1.7.2 Dimensionless Pi-Groups
		1.7.3 Windscreen Noise*
		1.7.4 Similitude Summary
	1.8 Precision, Accuracy, and Error Propagation
		1.8.1 Random Errors (Noise) and Relative Uncertainty
		1.8.2 Normal Error Function or the Gaussian Distribution
		1.8.3 Systematic Errors (Bias)
		1.8.4 Error Propagation and Covariance
		1.8.5 Significant Figures
	1.9 Least-Squares Fitting and Parameter Estimation
		1.9.1 Linear Correlation Coefficient
		1.9.2 Relative Error in the Slope
		1.9.3 Linearized Least-Squares Fitting
		1.9.4 Caveat for Data Sets with Small N*
		1.9.5 Best-Fit to Models with More Than Two Adjustable Parameters
	1.10 The Absence of Rigorous Mathematics
		Talk Like an Acoustician
	References
Part I: Vibrations
	Chapter 2: The Simple Harmonic Oscillator
		2.1 The Undamped Harmonic Oscillator
			2.1.1 Initial Conditions and the Phasor Representation
		2.2 The Lumped-Element Approximation
			2.2.1 Series and Parallel Combinations of Several Springs
			2.2.2 A Characteristic Speed
		2.3 Energy
			2.3.1 The Virial Theorem
			2.3.2 Rayleigh´s Method
			2.3.3 Gravitational Offset
			2.3.4 Adiabatic Invariance
		2.4 Damping and Free-Decay
			2.4.1 Viscous Damping and Mechanical Resistance
			2.4.2 Free-Decay Frequency and Quality Factor
			2.4.3 Critical Damping
			2.4.4 Thermal Equilibrium and Fluctuations
			2.4.5 Frictional (Coulomb) Damping*
		2.5 Driven Systems
			2.5.1 Force-Driven SHO
			2.5.2 Power Dissipation, the Decibel, and Resonance Bandwidth
			2.5.3 Resonance Tracking and the Phase-Locked Loop*
			2.5.4 Transient Response
			2.5.5 The Electrodynamic Loudspeaker
			2.5.6 Electrodynamic (Moving-Coil) Microphone
			2.5.7 Displacement-Driven SHO and Transmissibility
		2.6 Vibration Sensors
		2.7 Coupled Oscillators
			2.7.1 Two Identical Masses with Three Identical Springs
			2.7.2 Coupled Equations for Identical Masses and Springs
			2.7.3 Normal Modes and Normal Coordinates
			2.7.4 Other Initial Conditions
			2.7.5 General Solutions for Two Masses and Three Springs
			2.7.6 Driven Oscillators, Level Repulsion, and Beating
			2.7.7 String of Pearls
		2.8 The Not-So-Simple (?) Harmonic Oscillator
			Talk Like an Acoustician
		References
	Chapter 3: String Theory
		3.1 Waves on a Flexible String
		3.2 Pulse Reflections at a Boundary and the Utility of Phantoms
		3.3 Normal Modes and Standing Waves
			3.3.1 Idealized Boundary Conditions
			3.3.2 Consonance and Dissonance*
			3.3.3 Consonant Triads and Musical Scales*
		3.4 Modal Energy
			3.4.1 Nature Is Efficient
			3.4.2 Point Mass Perturbation
			3.4.3 Heavy Chain Pendulum (Nonuniform Tension)*
		3.5 Initial Conditions
			3.5.1 Total Modal Energy
		3.6 ``Imperfect´´ Boundary Conditions
			3.6.1 Example: Standing Wave Modes for M/ms = 5
			3.6.2 An Algebraic Approximation for the Mass-Loaded String
			3.6.3 The Resistance-Loaded String*
		3.7 Forced Motion of a Semi-Infinite String
		3.8 Forced Motion of a Finite String
			3.8.1 Displacement-Driven Finite String
			3.8.2 Mass-Loaded String in the Impedance Model
			3.8.3 Force-Driven Finite String
			3.8.4 An Efficient Driver/Load Interaction
		3.9 ``I´ve Got the World on a String ´´: Chapter Summary
			Talk Like an Acoustician
		References
	Chapter 4: Elasticity of Solids
		4.1 Hooke, Young, Poisson, and Fourier
		4.2 Isotropic Elasticity
			4.2.1 Bulk Modulus
			4.2.2 Modulus of Unilateral Compression
			4.2.3 Shear Modulus
			4.2.4 Two Moduli Provide a Complete (Isotropic) Description
		4.3 Real Springs
			4.3.1 Solids as Springs
			4.3.2 Flexure Springs
			4.3.3 Triangularly Tapered Cantilever Spring*
			4.3.4 Buckling
			4.3.5 Torsional Springs
			4.3.6 Coil Springs
		4.4 Viscoelasticity
			4.4.1 The Maxwell (Relaxation Time) Model
			4.4.2 Standard Linear Model (SLM) of Viscoelasticity
			4.4.3 Complex Stiffnesses and Moduli*
			4.4.4 Kramers-Kronig Relations
		4.5 Rubber Springs
			4.5.1 Effective Modulus
			4.5.2 Rubber-to-Glass Transition (Type I and Type II Rubbers)
			4.5.3 Transmissibility of Rubberlike Vibration Isolators
		4.6 Anisotropic (Crystalline) Elasticity*
		4.7 There Is More to Stiffness Than Just ``´´
			Talk Like an Acoustician
		References
	Chapter 5: Modes of Bars
		5.1 Longitudinal Waves in Thin Bars
			5.1.1 Longitudinal Waves in Bulk Solids
			5.1.2 The Quartz Crystal Microbalance
			5.1.3 Bodine´s ``Sonic Hammer´´
		5.2 Torsional Waves in Thin Bars
		5.3 Flexural Waves in Thin Bars
			5.3.1 Dispersion
			5.3.2 Flexural Wave Functions
			5.3.3 Flexural Standing Wave Frequencies
			5.3.4 Flexural Standing Wave Mode Shapes
			5.3.5 Rayleigh Waves*
		5.4 Resonant Determination of Elastic Moduli
			5.4.1 Mode-Selective Electrodynamic Excitation and Detection
			5.4.2 Bar Sample Size and Preparation
			5.4.3 Measured Resonance Spectra
			5.4.4 Effective Length Correction for Transducer Mass
			5.4.5 Modes of a Viscoelastic Bar
			5.4.6 Resonant Ultrasound Spectroscopy*
		5.5 Vibrations of a Stiff String*
		5.6 Harmonic Analysis
			Talk Like an Acoustician
		References
	Chapter 6: Membranes, Plates, and Microphones
		6.1 Rectangular Membranes
			6.1.1 Modes of a Rectangular Membrane
			6.1.2 Modal Degeneracy
			6.1.3 Density of Modes
		6.2 Circular Membranes
			6.2.1 Series Solution to the Circular Wave Equation
			6.2.2 Modal Frequencies and Density for a Circular Membrane
			6.2.3 Mode Similarities Illustrating Adiabatic Invariance
			6.2.4 Normal Modes of Wedges and Annular Membranes*
			6.2.5 Effective Piston Area for a Vibrating Membrane
			6.2.6 Normal Mode Frequencies of Tympani
			6.2.7 Pressure-Driven Circular Membranes
		6.3 Response of a Condenser Microphone
			6.3.1 Optimal Backplate Radius
			6.3.2 Limits on Polarizing Voltages and Electrostatic Forces
			6.3.3 Electret Condenser Microphone
		6.4 Vibrations of Thin Plates
			6.4.1 Normal Modes of a Clamped Circular Plate
		6.5 Flatland
			Talk Like an Acoustician
		References
Part II: Waves in Fluids
	Chapter 7: Ideal Gas Laws
		7.1 Two Ways of Knowing-Phenomenology and Microscopics
			7.1.1 Microscopic Models
			7.1.2 Phenomenological Models
			7.1.3 Adiabatic Equation of State for an Ideal Gas
			7.1.4 Adiabatic Temperature Change
		7.2 Specific Heats of Ideal Gases
			7.2.1 Monatomic (Noble) Gases
			7.2.2 Polyatomic Gases
		7.3 The Fundamental Equations of Hydrodynamics
			7.3.1 The Continuity Equation
			7.3.2 The Navier-Stokes (Euler) Equation
			7.3.3 The Entropy Equation
			7.3.4 Closure with the Equation of State
		7.4 Flashback
			Talk Like an Acoustician
		References
	Chapter 8: Nondissipative Lumped Elements
		8.1 Oscillations About Equilibrium
		8.2 Acoustical Compliance and the Continuity Equation
			8.2.1 The Continuity Equation
			8.2.2 Linearized Continuity Equation
			8.2.3 Acoustical Compliance
			8.2.4 The Gas Spring
		8.3 Hydrostatic Pressure
		8.4 Inertance and the Linearized Euler Equation
			8.4.1 The Venturi Tube
			8.4.2 The Linearized Euler Equation
			8.4.3 Acoustical Inertance
			8.4.4 Acoustical Mass
		8.5 The Helmholtz Resonance Frequency
			8.5.1 Helmholtz Resonator Network Analysis
			8.5.2 A 500-mL Boiling Flask
		8.6 DeltaEC Software
			8.6.1 Download DeltaEC
			8.6.2 Getting Started with DeltaEC (Thermophysical Properties)
			8.6.3 Creating planewave.out
			8.6.4 Running planewave.out
			8.6.5 Finding the Resonance Frequencies of planewave.out
			8.6.6 State Variable Plots (.sp)
			8.6.7 Modifying planewave.out to Create Flask500.out
			8.6.8 Interpreting the .out File
			8.6.9 The RPN Segment
			8.6.10 Power Flow and Dissipation in the 500 Ml Boiling Flask
			8.6.11 An ``Effective Length´´ Correction
			8.6.12 Incremental Plotting and the .ip File
			8.6.13 So Much More Utility in DeltaEC
		8.7 Coupled Helmholtz Resonators
		8.8 The Bass-Reflex Loudspeaker Enclosure
			8.8.1 Beranek´s Box Driven by a Constant Volume Velocity
			8.8.2 Loudspeaker-Driven Bass-Reflex Enclosure*
		8.9 Lumped Elements
			Talk like an Acoustician
		References
	Chapter 9: Dissipative Hydrodynamics
		9.1 The Loss of Time Reversal Invariance
		9.2 Ohm´s Law and Electrical Resistivity
		9.3 Thermal Conductivity and Newton´s Law of Cooling
			9.3.1 The Thermal Boundary Layer
			9.3.2 Adiabatic Compression Within a Bounded Volume
			9.3.3 Energy Loss in the Thermal Boundary Layer*
			9.3.4 Adiabatic vs. Isothermal Propagation in an Ideal Gas
		9.4 Viscosity
			9.4.1 Poiseuille Flow in a Pipe of Circular Cross-Section
			9.4.2 The Viscous Boundary Layer
			9.4.3 Viscous Drag in the Neck of a Helmholtz Resonator
			9.4.4 Quality Factors for a Helmholtz Resonator
		9.5 Kinetic Theory of Thermal and Viscous Transport
			9.5.1 Mean Free Path
			9.5.2 Thermal Conductivity of an Ideal Gas
			9.5.3 Viscosity of an Ideal Gas
			9.5.4 Prandtl Number of an Ideal Gas and Binary Gas Mixtures*
		9.6 Not a Total Loss
			Talk Like an Acoustician
		References
	Chapter 10: One-Dimensional Propagation
		10.1 The Transition from Lumped Elements to Waves in Fluids
		10.2 The Wave Equation
			10.2.1 General Solutions to the Wave Equation
		10.3 The Dispersion Relation (Phase Speed)
			10.3.1 Speed of Sound in Liquids
			10.3.2 Speed of Sound in Ideal Gases and Gas Mixtures
		10.4 Harmonic Plane Waves and Characteristic Impedance
		10.5 Acoustic Energy Density and Intensity
			10.5.1 Decibel Scales
			10.5.2 Superposition of Sound Levels (Rule for Adding Decibels)
			10.5.3 Anthropomorphic Frequency Weighting of Sound Levels
		10.6 Standing Waves in Rigidly Terminated Tubes
			10.6.1 Quality Factor in a Standing Wave Resonator
			10.6.2 Resonance Frequency in Closed-Open Tubes
		10.7 Driven Plane Wave Resonators
			10.7.1 Electroacoustic Transducer Sensitivities
			10.7.2 The Principle of Reciprocity
			10.7.3 In Situ Reciprocity Calibration
			10.7.4 Reciprocity Calibration in Other Geometries
			10.7.5 Resonator-Transducer Interaction
			10.7.6 Electrodynamic Source Coupling Optimization*
		10.8 Junctions, Branches, and Filters
			10.8.1 Abrupt Discontinuities and the Acoustic Admittance
			10.8.2 Tuned Band-Stop Filter
			10.8.3 Stub Tuning
		10.9 Quasi-One-Dimensional Propagation (Horns)
			10.9.1 Semi-infinite Exponential Horns
			10.9.2 Salmon Horns*
			10.9.3 Horns of Finite Length*
				Talk Like an Acoustician
		References
	Chapter 11: Reflection, Transmission, and Refraction
		11.1 Normal Incidence
		11.2 Three Media
			11.2.1 A Limp Diaphragm Separating Two Gases
			11.2.2 An Impedance Matching Antireflective Layer
			11.2.3 The ``Mass Law´´ for Sound Transmission Through Walls
			11.2.4 Duct Constriction/Expansion Low-Pass Filters
		11.3 Snell´s Law and Fermat´s Principle
			11.3.1 Total Internal Reflection
			11.3.2 The Rayleigh Reflection Coefficient
		11.4 Constant Sound Speed Gradients
			11.4.1 Constant Gradient´s Equivalence to Solid Body Rotation
			11.4.2 Sound Channels
			11.4.3 Propagation Delay*
			11.4.4 Under Ice Propagation
			11.4.5 Sound Focusing
				Talk Like an Acoustician
		References
	Chapter 12: Radiation and Scattering
		12.1 Sound Radiation and the ``Causality Sphere´´
		12.2 Spherically Diverging Sound Waves
			12.2.1 Compact Monopole Radiation Impedance
			12.2.2 Compact Monopole Acoustic Transfer Impedance
			12.2.3 General Multipole Expansion*
		12.3 Bubble Resonance
			12.3.1 Damping of Bubble Oscillations
		12.4 Two In-Phase Monopoles
			12.4.1 The Method of Images
		12.5 Two Out-Of-Phase Compact Sources (Dipoles)
			12.5.1 Dipole Radiation
			12.5.2 Cardioid (Unidirectional) Radiation Pattern
			12.5.3 Pressure Gradient Microphones
			12.5.4 The DIFAR Directional Sonobuoy
		12.6 Translational Oscillations of an Incompressible Sphere
			12.6.1 Scattering from a Compact Density Contrast
			12.6.2 Scattering from a Compact Compressibility Contrast
			12.6.3 Scattering from a Single Bubble or a Swim Bladder
			12.6.4 Multiple Scattering in the ``Effective Medium´´ Approximation
		12.7 N-Element Discrete Line Array
			12.7.1 Beam Steering and Shading
			12.7.2 Continuous Line Array
		12.8 Baffled Piston
			12.8.1 Rayleigh Resolution Criterion
			12.8.2 Directionality and Directivity
			12.8.3 Radiation Impedance of a Baffled Circular Piston
			12.8.4 Radiation Impedance of a Baffled Rectangular Piston*
			12.8.5 On-Axis Near-Field Pressure from a Circular Baffled Piston*
		12.9 Radiation Impedance of an Unbaffled Piston
		12.10 Linear Superposition
			Talk Like an Acoustician
		References
	Chapter 13: Three-Dimensional Enclosures
		13.1 Separation of Variables in Cartesian Coordinates
			13.1.1 Rigid-Walled Rectangular Room
			13.1.2 Mode Characterization
			13.1.3 Mode Excitation
			13.1.4 Density of Modes
		13.2 Statistical Energy Analysis
			13.2.1 The Sabine Equation
			13.2.2 Critical Distance and the Schroeder Frequency
		13.3 Modes of a Cylindrical Enclosure
			13.3.1 Pressure Field Within a Rigid Cylinder and Normal Modes
			13.3.2 Modal Density Within a Rigid Cylinder
			13.3.3 Modes of a Rigid-Walled Toroidal Enclosure*
			13.3.4 Modal Degeneracy and Mode Splitting
			13.3.5 Modes in Non-separable Coordinate Geometries
		13.4 Radial Modes of Spherical Resonators
			13.4.1 Pressure-Released Spherical Resonator
			13.4.2 Rigid-Walled Spherical Resonator
		13.5 Waveguides
			13.5.1 Rectangular Waveguide
			13.5.2 Phase Speed and Group Speed
			13.5.3 Driven Waveguide
			13.5.4 Cylindrical Waveguide
			13.5.5 Attenuation from Thermoviscous Boundary Losses
				Talk Like an Acoustician
		References
	Chapter 14: Attenuation of Sound
		14.1 An Almost Correct Expression for Viscous Attenuation
		14.2 Bulk Thermoviscous Attenuation in Fluids
		14.3 Classical Thermoviscous Attenuation
		14.4 The Time-Dependent Equation of State
		14.5 Attenuation due to Internal Relaxation Times
			14.5.1 Relaxation Attenuation in Gases and Gas Mixtures
			14.5.2 Relaxation Attenuation in Fresh and Salt Water
		14.6 Transmission Loss
			14.6.1 Short and Very Short Wavelengths
			14.6.2 Very Long Wavelengths
		14.7 Quantum Mechanical Manifestations in Classical Mechanics
			Talk Like an Acoustician
		References
Part III: Extensions
	Chapter 15: Nonlinear Acoustics
		15.1 Surf´s Up
			15.1.1 The Grüneisen Parameter
			15.1.2 The Virial Expansion and B/2A
			15.1.3 Anomalous Distortion*
			15.1.4 The Gol´dberg Number
			15.1.5 Stable Sawtooth Waveform Attenuation
		15.2 Weak Shock Theory and Harmonic Distortion
			15.2.1 The Order Expansion
			15.2.2 Trigonometric Expansion of the Earnshaw Solution
			15.2.3 Higher Harmonic Generation
		15.3 The Phenomenological Model
			15.3.1 The (Nondissipative) Nonlinear Wave Equation
			15.3.2 Geometrical Resonance (Phase Matching)
			15.3.3 Intermodulation Distortion and the Parametric End-Fire Array
			15.3.4 Resonant Mode Conversion
		15.4 Non-zero Time-Averaged Effects
			15.4.1 The Second-Order Pressure in an Adiabatic Compression
			15.4.2 The Bernoulli Pressure
			15.4.3 The Rayleigh Disk
			15.4.4 Radiation Pressure
			15.4.5 Acoustic Levitation in Standing Waves
			15.4.6 Adiabatic Invariance and the Levitation Force
			15.4.7 Levitation Superstability (``Acoustic Molasses´´)
		15.5 Beyond the Linear Approximation
			Talk Like an Acoustician
		References
Appendices
	Appendix A: Useful Physical Constants and Conversion Factors
	Appendix B: Resonator Quality Factor
	Appendix C: Bessel Functions of the First Kind
	Appendix D: Trigonometric Functions
	Appendix E: Hyperbolic Functions
Index