Fundamentals of Physical Acoustics

by Blackstock, David T.

• ISBN13: 9780471319795
• ISBN10: 0471319791
• Edition: 1st
• Format: Hardcover
• Copyright: 2000-04-24
• Publisher: Wiley-Interscience

Summary

AN AUTHORITATIIVE, UP-TO-DATE INTRODUCTION TO PHYSICAL ACOUSTICS Easy to read and understand, Fundamentals of Physical Acoustics fills a long-standing need for an acoustics text that challenges but does not overpower graduate students in engineering and physics. Mathematical results and physical explanations go hand in hand, and a unique feature of the book is the balance it strikes between time-domain and frequency-domain presentations. Fundamentals of Physical Acoustics is intended for a two-semester, first-year graduate course, but is also suitable for advanced undergraduates. Emphasis on plane waves in the first part of the book keeps the mathematics simple yet accommodates a broad range of topics: propagation, reflection and transmission, normal modes and simple waveguides for rectilinear geometries, horns, inhomogeneous media, and sound absorption and dispersion. The second part of the book is devoted to a more rigorous development of the wave equation, spherical and cylindrical waves (including the more advanced mathematics required), advanced waveguides, baffled piston radiation, diffraction (treated in the time domain), and arrays. Applications and examples are drawn from: * Atmospheric acoustics * Noise control * Underwater acoustics * Engineering acoustics * Acoustical measurements Supplemented with more than 300 graphs and figures as well as copious end-of-chapter problems, Fundamentals of Physical Acoustics is also an excellent professional reference for engineers and scientists.

Author Biography

DAVID T. BLACKSTOCK is a professor in the Department of Mechanical Engineering at the University of Texas at Austin. He is a past president of the Acoustical Society of America and has been awarded its Gold Medal.

Table of Contents

Preface	xix
Introduction	1	(64)
What Is a Wave?	1	(2)
Plane Waves: Some Basic Solutions	3	(15)
General Solution of the Wave Equation	4	(6)
Free Waves	10	(4)
Forced Waves	14	(2)
Relation between Derivatives for a Progressive Wave	16	(2)
Derivation of Wave Equations. Impedance	18	(21)
Electrical Transmission Line	18	(4)
Waves on a String	22	(5)
Sound Waves	27	(12)
Spherical and Cylindrical Sound Waves of One Dimension	39	(5)
Three-Dimensional Wave Equation	40	(1)
Solutions for One-Dimensional Waves	41	(1)
Sound from a Pulsating Sphere	42	(2)
Signals, Impedance, Intensity and Power, and Levels	44	(21)
Time and Frequency Domains	44	(2)
Impedance	46	(2)
Intensity and Sound Power	48	(3)
Sound Pressure Level and Other Levels	51	(4)
References	55	(1)
Problems	55	(10)
Detailed Development of the Acoustical Wave Equation	65	(43)
Conservation Equations and Constitutive Relation	65	(19)
Equation of Continuity	65	(4)
Momentum Equation	69	(8)
Energy Equation	77	(3)
Equation of State (Constitutive Relation)	80	(2)
Entropy Equation	82	(1)
Summary and Discussion	83	(1)
Nonlinear Wave Equation	84	(7)
Introduction	84	(2)
Plane Progressive Waves of Finite Amplitude	86	(3)
Second-Harmonic Distortion	89	(2)
Sum- and Difference-Frequency (Intermodulation) Distortion	91	(1)
Small-Signal Wave Equation	91	(17)
Lossless Medium at Rest	91	(2)
Lossless Medium Moving with Constant Velocity	93	(2)
Lossless Medium in a Gravitational Field	95	(1)
Viscous Fluid	96	(1)
Viscous, Thermally Conducting Fluid	97	(1)
Relaxing Fluid	98	(1)
References	98	(1)
Problems	99	(9)
Reflection and Transmission of Normally Incident Plane Waves of Arbitrary Waveform	108	(22)
Reflection and Transmission Coefficients for an Interface between Two Ideal Fluids	108	(4)
Pressure Signals	109	(2)
Sound Power	111	(1)
Transmission Loss	112	(1)
Special Cases	112	(2)
Rigid Wall	112	(1)
Pressure Release Surface	113	(1)
Matched Impedance Interface	114	(1)
Change in Cross-Sectional Area	114	(2)
Examples	116	(14)
Rectangular Pulse in an Air-Filled Tube of Finite Length	117	(2)
Shock Tube	119	(2)
Bursting Balloon	121	(4)
References	125	(1)
Problems	125	(5)
Normal Incidence Continued: Steady-State Analysis	130	(56)
Introduction	130	(4)
Single Impedance Termination	134	(10)
Pressure Release Termination (Zn=0)	134	(4)
Rigid Termination (Zn=∞)	138	(1)
General Resistive Termination	139	(1)
General Impedance Termination	140	(4)
Change in Cross-Sectional Area	144	(1)
Lumped-Element Approximation	144	(12)
Electrical Analogs	144	(1)
Short Closed Cavity	145	(6)
End Correction for an Open Tube	151	(2)
Short Open Cavity	153	(1)
Helmholtz Resonator	153	(3)
Orifice	156	(1)
Examples	156	(7)
Side Branches, Filters	156	(4)
Probe Tube Microphone	160	(3)
Three-Medium Problems	163	(8)
Three Different Media, Constant Cross Section	163	(5)
Cross Sections Different for the Three Media	168	(2)
Sound Power Reflection and Transmission Coefficients	170	(1)
Wall Transmission Loss: Lumped-Element Approach	171	(15)
References	173	(1)
Problems	174	(12)
Transmission Phenomena: Oblique Incidence	186	(32)
Simple Derivation of Snell's Law and Specular Reflection	186	(3)
Plane Interface Separating Two Fluids	189	(9)
Alternative Derivation of Snell's Law; R, T, and τ Coefficients	190	(3)
Special Cases	193	(5)
Transmission through Panels at Oblique Incidence	198	(10)
Transmission Dominated by Panel Mass: The Mass Law	200	(3)
Panel Stiffness: The Coincidence Effect	203	(5)
Composite Walls	208	(10)
References	211	(1)
Problems	211	(7)
Normal Modes in Cartesian Coordinates: Strings, Membranes, Rooms, and Rectangular Waveguides	218	(32)
Vibrating String (and other One-Dimensional Problems)	218	(11)
String with Fixed Ends	219	(7)
Other Boundary Conditions	226	(1)
The Struck String	227	(2)
Vibrating Membrane	229	(4)
Sound in a Rectangular Enclosure	233	(3)
Rectangular Waveguide	236	(14)
Membrane Waveguide	236	(2)
Forward Traveling Waves, Phase Velocity, and Cutoff	238	(2)
Physical Interpretation	240	(2)
Source Conditions	242	(1)
References	243	(1)
Problems	244	(6)
Horns	250	(23)
Webster Horn Equation	251	(3)
Continuity Equation	251	(1)
Momentum Equation	252	(2)
Webster Horn Equation	254	(1)
Example: Exponential Horn	254	(3)
Exponential Horn Equation and Solution	254	(1)
Amplitude Decay and Phase Velocity	255	(2)
Impedance, Power Transmitted, and Transmission Factor	257	(3)
Impedance and Power	258	(1)
Conical Horn	259	(1)
Transmission Factor	260	(1)
More General Approach: WKB Method	260	(6)
Application to the Horn Equation: Direct Approach	262	(1)
Modified Approach	263	(1)
Impedance and Transmission Factor	264	(1)
Examples	265	(1)
Horn Duals	266	(7)
References	267	(1)
Problems	268	(5)
Propagation in Stratified Media	273	(25)
Static Properties of the Atmosphere and the Ocean	274	(4)
Atmosphere	274	(2)
Ocean	276	(2)
Vertical Propagation of Plane Waves	278	(6)
One-Dimensional Wave Equation	278	(2)
Vertical Propagation through an Isothermal Atmosphere	280	(1)
General Solution by Means of the WKB Method	281	(3)
Ray Theory	284	(14)
Ray Paths	284	(4)
Rays in a Fluid Having a Linear Sound Speed Profile	288	(4)
Time of Travel along a Ray Path	292	(2)
References	294	(1)
Problems	294	(4)
Propagation in Dissipative Fluids: Absorption and Dispersion	298	(37)
Introduction	298	(5)
Viscosity and Heat Conduction	303	(12)
Viscous Fluids	304	(2)
Thermally Conducting Fluids	306	(7)
Thermoviscous Fluids	313	(2)
Relaxation	315	(7)
Introduction	315	(2)
Equation of State	317	(1)
Wave Equation	318	(1)
Dispersion Relation	318	(4)
Boundary-Layer Absorption (and Dispersion)	322	(3)
Physical Phenomenon: Viscous Boundary Layer	322	(1)
Thermal Boundary Layer	323	(1)
Effect of the Two Boundary Layers	324	(1)
Summary of Sound Absorption in Fluids	325	(10)
Viscous Fluids	325	(1)
Thermally Conducting Fluids	326	(1)
Thermoviscous Fluids	326	(1)
Relaxing Fluids	326	(1)
Boundary-Layer Absorption: Thermoviscous Fluids	327	(1)
References	327	(1)
Problems	328	(7)
Spherical Waves	335	(51)
Introduction	335	(2)
Solution by Separation of Variables	337	(15)
Legendre Polynomials	338	(3)
Spherical Bessel Functions	341	(3)
Spherical Hankel Functions	344	(1)
Summary of Solutions for Axially Symmetric Wave Motion	345	(1)
Most General Spherical Waves; Spherical Harmonics	346	(3)
Example: Bipolar Pulsating Sphere	349	(3)
Standing Spherical Waves: Enclosure Problems	352	(4)
Pressure Release Sphere	353	(2)
Hollow Sphere	355	(1)
Radiation Problems	356	(30)
Introduction: Multipole Expansion	356	(2)
Monopoles	358	(9)
Dipoles	367	(8)
References	375	(1)
Problems	376	(10)
Cylindrical Waves	386	(34)
Solution of the Wave Equation in Cylindrical Coordinates	386	(12)
Solution by Separation of Variables	387	(2)
Properties of Bessel Functions	389	(9)
Circular Membrane	398	(6)
Introduction	398	(2)
Example: Membrane with Uniform Initial Displacement	400	(1)
Variations	401	(3)
Three-Dimensional Cylindrical Coordinates	404	(16)
Enclosure Problems	404	(3)
Radiation Problems	407	(6)
References	413	(1)
Problems	413	(7)
Waveguides	420	(20)
Introduction	420	(1)
Rectangular Waveguide	421	(7)
General Solution	421	(2)
Source Conditions and Mode Excitation	423	(1)
Example	424	(3)
Pressure Release Walls	427	(1)
Phase and Group Velocity	427	(1)
Cylindrical Waves in Waveguides	428	(12)
Cylindrical Tube	429	(1)
Parallel Planes	430	(2)
References	432	(1)
Problems	433	(7)
Radiation from a Baffled Piston	440	(32)
General Solution: The Rayleigh Integral	441	(5)
Time-Harmonic Piston Vibration	442	(1)
Example: Ring Piston	442	(3)
Circular Piston (Disk)	445	(1)
Farfield Radiation	446	(6)
Rayleigh Distance	447	(2)
Size of ka	449	(1)
First Null, Minor-Lobe Suppression, Beamwidth, and Phase	450	(1)
Intensity, Power, and Source Level	451	(1)
Pressure Field on the Axis	452	(5)
Transition to the Farfield	454	(1)
Nearfield Structure	454	(1)
Intensity	455	(2)
Pressure on the Face of the Piston	457	(3)
Transient Radiation from a Piston	460	(3)
Signal on the Axis	460	(1)
Farfield	461	(2)
Nonuniform Piston	463	(9)
References	465	(1)
Problems	465	(7)
Diffraction	472	(23)
Introduction	472	(1)
Helmholtz-Kirchhoff Integral Theorem	473	(3)
Derivation	473	(2)
Time Domain Version	475	(1)
Circular Aperture	476	(5)
Plane Wave Normally Incident on a Circular Aperture	477	(3)
Spherical Wave Incident on a Circular Aperture	480	(1)
Reflection by a Rigid Disk	481	(5)
Babinet's Principle	486	(9)
References	489	(1)
Problems	489	(6)
Arrays	495	(15)
Directivity: Nomenclature and Definitions	495	(4)
Array of Two Point Sources	499	(3)
Array of N Point Sources	502	(2)
Continuous Line Array	504	(2)
Array of Directional Sources: Product Theorem	506	(4)
References	506	(1)
Problems	506	(4)
Appendix A Elastic Constants, Velocity of Sound, and Characteristic Impedance	510	(3)
Appendix B Absorption Formulas for the Atmosphere and Ocean	513	(6)
Atmosphere	513	(3)
Ocean	516	(3)
References	518	(1)
Appendix C Absorption due to Tube Wall Boundary-Layer Effects	519	(7)
Viscous Boundary Layer	520	(4)
Quasi-Plane-Wave Equation	524	(1)
Effect of the Thermal Boundary Layer	525	(1)
References	525	(1)
Appendix D Solution of Legendre's Equation by Power Series	526	(2)
Appendix E Directivity and Impedance Functions for a Circular Piston	528	(3)
Index	531