PRACTICAL PHYSICS: MOLECULAR PHYSICS & SOUND
CONTENTS THE WAVE THEORY OF SOUND A LITTLE HISTORY THE CONSERVATION OF MASS EULER’S EQUATION FOR A FLUID PRESSURE–DENSITY RELATIONS LAPLACE’S HYPOTHESIS INTERPRETATION IN TERMS OF ENTROPY INCORPORATION OF HEAT CONDUCTION INTO FLUID DYNAMICS EQUATIONS OF LINEAR ACOUSTICS THE WAVE EQUATION THE VELOCITY POTENTIAL PLANE TRAVELING WAVES PROCESSES OCCURRING DURING PASSAGE OF A SOUND WAVE WAVES OF CONSTANT FREQUENCY TIME AVERAGE OF A PRODUCT SPATIALLY DEPENDENT COMPLEX AMPLITUDES PLANE WAVES OF CONSTANT FREQUENCY SPEED OF SOUND AND AMBIENT DENSITY SPEED OF SOUND IN GASES ACOUSTIC PROPERTIES OF LIQUIDS ADIABATIC VERSUS ISOTHERMAL SPEEDS ENERGY, INTENSITY, AND SOURCE POWER ACOUSTIC-ENERGY COROLLARY ENERGY CONSERVATION IN FLUIDS ACOUSTIC POWER OF SOURCES SPHERICAL WAVES SPHERICAL SPREADING OF ACOUSTIC ENERGY SPHERICALLY SYMMETRIC SOLUTION OF THE WAVE EQUATION FLUID VELOCITY IN A SPHERICALLY SYMMETRIC WAVE INTENSITY AND ENERGY DENSITY FIELD AT LARGE DISTANCES FROM SOURCE OF FINITE EXTENT PROBLEMS QUANTITATIVE MEASURES OF SOUND FREQUENCY CONTENT OF SOUNDS FREQUENCY BANDS FREQUENCY PARTITIONING OF MEAN SQUARED PRESSURE FREQUENCY PARTITIONING OF INTENSITY, ACOUSTIC POWER, AND ENERGY DENSITY PROPORTIONAL FREQUENCY BANDS STANDARD FREQUENCIES AND BANDS EQUALLY TEMPERED MUSICAL SCALES LEVELS AND THE DECIBEL SOUND-PRESSURE LEVELS LEVELS AND SOUND-PRESSURE RATIOS LOGARITHMS AND ANTILOGARITHMS HISTORY OF THE DECIBEL INTENSITY AND POWER LEVELS FREQUENCY WEIGHTING AND FILTERS FREQUENCY WEIGHTING FUNCTIONS LINEAR FILTERS COMBINING OF LEVELS MUTUALLY INCOHERENT SOUND SOURCES FOURIER SERIES AND LONG-DURATION SOUNDS SPECTRAL DENSITY LEVELS AND SPECTRAL DENSITY WHITE AND PINK NOISE TRANSIENT WAVEFORMS DIRAC DELTA FUNCTION SOUND-EXPOSURE SPECTRAL DENSITY TRANSFER FUNCTIONS STATIONARY ERGODIC PROCESSES WIENER–KHINTCHINE THEOREM BIAS AND VARIANCE RE?ECTION, TRANSMISSION, AND EXCITATION OF PLANE WAVES BOUNDARY CONDITIONS AT IMPENETRABLE SURFACES STATIONARY SURFACES VIBRATING SURFACES CONTINUITY OF NORMAL COMPONENT OF DISPLACEMENT PLANE-WAVE RE?ECTION AT A FLAT RIGID SURFACE SPECI?C ACOUSTIC IMPEDANCE PLANE TRAVELING WAVES AND SPECI?C ACOUSTIC IMPEDANCE PLANE-WAVE RE?ECTION AT A SURFACE WITH FINITE SPECI?C IMPEDANCE LOCALLY REACTING SURFACES THEORY OF THE IMPEDANCE TUBE RADIATION OF SOUND BY A VIBRATING PISTON WITHIN A TUBE CAUSALITY TUBE WITH RIGID END: RESONANCE CONSTANT-FREQUENCY OSCILLATIONS TUBE WITH IMPEDANCE BOUNDARY CONDITION AT END THE Q OF A RESONANCE SOUND RADIATION BY TRAVELING FLEXURAL WAVES SOUND GENERATED BY SUPERSONIC FLEXURAL WAVES TRACE-VELOCITY MATCHING PRINCIPLE OUTGOING VERSUS INCOMING WAVES ACOUSTIC DISTURBANCES CREATED BY SUBSONIC FLEXURAL WAVES THE COINCIDENCE FREQUENCY SPECI?C RADIATION IMPEDANCE RE?ECTION AND TRANSMISSION AT AN INTERFACE BETWEEN TWO FLUIDS WATER–AIR INTERFACES TRANSIENT RE?ECTION MULTILAYER TRANSMISSION AND RE?ECTION TRANSMISSION THROUGH THIN SOLID SLABS, PLATES, AND BLANKETS TRANSMISSION LOSS SLAB SPECI?C IMPEDANCE OBLIQUE-INCIDENCE MASS LAW TRANSMISSION THROUGH EULER–BERNOULLI PLATES TRANSMISSION THROUGH POROUS BLANKETS RADIATION FROM VIBRATING BODIES RADIALLY OSCILLATING SPHERE LOW-FREQUENCY APPROXIMATION TRANSVERSELY OSCILLATING RIGID SPHERE FORCE EXERTED BY TRANSVERSELY OSCILLATING SPHERE SMALL-KA APPROXIMATION MONOPOLES AND GREEN’S FUNCTIONS CONCEPT OF A POINT SOURCE POINT MASS SOURCE GREEN’S FUNCTIONS DIPOLES AND QUADRUPOLES DIPOLES POINT FORCE IN A FLUID QUADRUPOLES MULTIPOLE EXPANSIONS UNIQUENESS OF SOLUTIONS OF ACOUSTIC BOUNDARY-VALUE PROBLEMS POISSON’S THEOREM AND ITS IMPLICATIONS CLOSED REGIONS UNIQUENESS AND OPEN REGIONS SOMMERFELD RADIATION CONDITION UNIQUENESS OF CONSTANT-FREQUENCY FIELDS THE KIRCHHOFF–HELMHOLTZ INTEGRAL THEOREM MULTIPOLE EXPANSIONS OF THE KIRCHHOFF–HELMHOLTZ INTEGRAL SOUND RADIATION FROM SMALL VIBRATING BODIES RADIATION FROM A CIRCULAR DISK OBLATE-SPHEROIDAL COORDINATES SOLUTIONS OF LAPLACE’S EQUATION DETERMINATION OF THE OUTER SOLUTION RECIPROCITY IN ACOUSTICS RECIPROCITY IN VIBRATING SYSTEMS RECIPROCITY AND THE LINEAR ACOUSTIC EQUATIONS INTERCHANGE OF SOURCE AND LISTENER RECIPROCITY AND GREEN’S FUNCTIONS TRANSDUCERS AND RECIPROCITY RADIATION FROM SOURCES NEAR AND ON SOLID SURFACES SOURCES NEAR PLANE RIGID BOUNDARIES IMAGE SOURCES REMARKS CONCERNING ACOUSTIC POWER AND SPHERICAL SPREADING CASES WHEN MORE THAN ONE WALL IS PRESENT DEPENDENCE OF ACOUSTIC FAR FIELD AND NET ACOUSTIC POWER OUTPUT ON DISTANCE FROM A WALL SOURCES MOUNTED ON WALLS: THE RAYLEIGH INTEGRAL; FRESNEL–KIRCHHOFF THEORY OF DIFFRACTION BY AN APERTURE GREEN’S-FUNCTION DERIVATION OF RAYLEIGH INTEGRAL FRESNEL–KIRCHHOFF THEORY OF DIFFRACTION LOW-FREQUENCY RADIATION FROM SOURCES MOUNTED ON WALLS PRESSURE ON VIBRATING CIRCULAR PISTON AT LOW FREQUENCIES FORCE EXERTED BY THE SLOWLY OSCILLATING BAF?ED PISTON RADIATION IMPEDANCE OF BAF?ED-PISTON RADIATORS ELECTROACOUSTIC SIGNI?CANCE OF RADIATION IMPEDANCE EVALUATION OF RADIATION IMPEDANCE FOR A BAF?ED CIRCULAR PISTON FAR-FIELD RADIATION FROM LOCALIZED WALL VIBRATIONS TRANSIENT SOLUTION FOR BAF?ED CIRCULAR PISTON FIELD ON AND NEAR THE SYMMETRY AXIS FIELD ON SYMMETRY AXIS FIELD NEAR SYMMETRY AXIS TRANSITION TO THE FAR FIELD PROPERTIES OF THE DIFFRACTION INTEGRAL FIELD NEAR EDGE OF MAIN BEAM CHARACTERISTIC SINGLE-EDGE DIFFRACTION PATTERN FIELD FAR OUTSIDE THE CENTRAL BEAM ROOM ACOUSTICS THE SABINE–FRANKLIN–JAEGER THEORY OF REVERBERANT ROOMS ENERGY-CONSERVATION EQUATION FOR ROOMS SPATIAL UNIFORMITY REVERBERATION TIME SABINE’S EQUATION DIFFUSE SOUND FIELDS EQUIVALENT AREA OF OPEN WINDOWS ABSORBING POWER OF OBJECTS AND PERSONS SOME MODI?CATIONS MEAN FREE PATH LIMITATIONS OF SABINE’S EQUATION NORRIS–EYRING REVERBERATION TIME ROOMS WITH ASYMMETRIC ABSORPTION THE ROOM CONSTANT APPLICATIONS OF THE SABINE–FRANKLIN–JAEGER THEORY DESIGN AND CORRECTION OF ROOMS MEASUREMENT OF ABSORPTION COEF?CIENTS AND REVERBERATION TIMES MEASUREMENT OF SOURCE POWER SIMULTANEOUS CONVERSATIONS IN A REVERBERANT ROOM COUPLED ROOMS AND LARGE ENCLOSURES TRANSMISSION OF REVERBERANT SOUND THROUGH A PANEL TRANSMISSION OUT THROUGH AN OPEN WINDOW THEORY OF LARGE ENCLOSURES COUPLED ROOMS REVERBERANT DECAY IN COUPLED ROOMS THE MODAL THEORY OF ROOM ACOUSTICS THE EIGENVALUE PROBLEM MODES FOR A RECTANGULAR ROOM ORTHOGONALITY OF MODAL EIGENFUNCTIONS MODAL EXPANSION OF FUNCTIONS FIELD OF A POINT SOURCE IN A ROOM WITH WALLS OF LARGE IMPEDANCE ACOUSTIC ENERGY IN A ROOM MODAL DESCRIPTION OF POWER INJECTION HIGH-FREQUENCY APPROXIMATIONS THE MODAL DENSITY THE SCHROEDER CUTOFF FREQUENCY APPROXIMATION OF MODAL SUMS BY INTEGRALS MODAL AVERAGES OF SQUARES OF EIGENFUNCTIONS EVALUATION OF MODAL INTEGRALS STATISTICAL ASPECTS OF ROOM ACOUSTICS FREQUENCY CORRELATION THE POISSON DISTRIBUTION EFFECT OF FINITE-FREQUENCY BANDWIDTH SPATIAL CORRELATIONS IN DIFFUSE SOUND FIELDS THE SPATIAL AUTOCORRELATION FUNCTION FOR ACOUSTIC PRESSURE SPATIAL AVERAGING FREQUENCY AVERAGING VERSUS SPATIAL AVERAGING LOW-FREQUENCY MODELS OF SOUND TRANSMISSION GUIDED WAVES DUCT CROSS-SECTIONAL EIGENFUNCTIONS DUCT WITH RECTANGULAR CROSS SECTION DUCT WITH CIRCULAR CROSS SECTION CUTOFF FREQUENCIES AND EVANESCENT MODES POINT SOURCE IN A DUCT LUMPED-PARAMETER MODELS VOLUME VELOCITY AND AVERAGE PRESSURE ACOUSTIC IMPEDANCE ACOUSTICAL TWO-PORTS CONTINUOUS-VOLUME-VELOCITY TWO-PORT CONTINUOUS-PRESSURE TWO-PORT GUIDELINES FOR SELECTING LUMPED-PARAMETER MODELS CONTINUITY OF PRESSURE CONTINUITY OF VOLUME VELOCITY RE?ECTION AND TRANSMISSION AT A JUNCTION HELMHOLTZ RESONATORS AND OTHER EXAMPLES THE HELMHOLTZ RESONATOR HELMHOLTZ RESONATOR AS A SIDE BRANCH COMPOSITE EXAMPLE ORI?CES MATCHED-ASYMPTOTIC-EXPANSION SOLUTION FOR ORI?CE TRANSMISSION ACOUSTIC-RADIATION RESISTANCE HELMHOLTZ RESONATOR WITH BAF?ED OPENING ACOUSTIC INERTANCE OF A CIRCULAR ORI?CE IN A THIN PLATE DIFFRACTION OF PLANE WAVE BY A CIRCULAR ORI?CE ESTIMATION OF ACOUSTIC INERTANCES AND END CORRECTIONS PRINCIPLE OF MINIMUM KINETIC ENERGY PRINCIPLE OF MINIMUM ACOUSTIC INERTANCE EFFECT OF RELAXING OF CONSTRAINTS LOWER BOUND FOR ACOUSTIC INERTANCE FLANGED OPENING IN A DUCT CIRCULAR ORI?CE IN A PLATE OF FINITE THICKNESS END CORRECTIONS EFFECTIVE NECK LENGTHS OF HELMHOLTZ RESONATORS BOUNDARY CONDITIONS AT OPEN ENDS OF DUCTS MUF?ERS AND ACOUSTIC FILTERS THE TRANSMISSION MATRIX AND ITS CONSEQUENCES INSERTION LOSS REACTIVE AND DISSIPATIVE MUF?ERS HELMHOLTZ RESONATORS AS FILTERS EXPANSION-CHAMBER MUF?ER COMMERCIAL MUF?ER DESIGNS HORNS THE WEBSTER HORN EQUATION SALMON’S FAMILY OF HORNS CONCEPT OF A SEMI-IN?NITE HORN THE CUTOFF FREQUENCY OTHER CONSIDERATIONS IN HORN DESIGN RAY ACOUSTICS WAVEFRONTS, RAYS, AND FERMAT’S PRINCIPLE RAY PATHS IN MOVING MEDIA FERMAT’S PRINCIPLE RECTILINEAR SOUND PROPAGATION PARAMETRIC DESCRIPTION OF WAVEFRONTS VARIATION OF PRINCIPAL RADII OF CURVATURE ALONG A RAY CAUSTICS REFRACTION IN INHOMOGENEOUS MEDIA REFRACTION BY SOUND-SPEED GRADIENTS RAYS IN A MEDIUM WITH CONSTANT-SOUND-SPEED GRADIENT REFRACTION BY WIND GRADIENTS RAYS IN STRATI?ED MEDIA THE RAY INTEGRALS CHANNELING OF RAY PATHS RAYS IN FLUIDS WITHOUT AMBIENT FLOW ABNORMAL SOUND AMPLITUDE VARIATION ALONG RAYS WAVE AMPLITUDES IN HOMOGENEOUS MEDIA ENERGY CONSERVATION ALONG RAYS WAVE AMPLITUDES IN MOVING MEDIA LINEAR ACOUSTICS EQUATIONS FOR MOVING MEDIA CONSERVATION OF WAVE ACTION THE BLOKHINTZEV INVARIANT SOURCE ABOVE AN INTERFACE SOUND FIELD ABOVE THE INTERFACE FIELD BELOW THE INTERFACE RE?ECTION FROM CURVED SURFACES GENERAL GEOMETRICAL CONSIDERATIONS RAY-TUBE AREA AFTER RE?ECTION ECHOES FROM CURVED SURFACES SOUND BEAM INCIDENT ON A SPHERE SCATTERING AND DIFFRACTION BASIC SCATTERING CONCEPTS SCATTERING BY A RIGID OBJECT SCATTERING CROSS SECTION HIGHER-FREQUENCY SCATTERING SCATTERING BY INHOMOGENEITIES SPHERICAL INHOMOGENEITY INERTIA EFFECT FOR FREELY SUSPENDED PARTICLE RESONANT SCATTERING MONOSTATIC AND BISTATIC SCATTERING: MEASUREMENT CON?GURATIONS MONOSTATIC PULSE-ECHO SOUNDING INHOMOGENEITIES AND THE BORN APPROXIMATION SCATTERING VOLUMES DELIMITED BY ELECTROACOUSTIC TRANSDUCERS ACOUSTIC RADAR EQUATION INCOHERENT SCATTERING THE ECHOSONDE EQUATION THE DOPPLER EFFECT DOPPLER SHIFT FOR A MOVING SOURCE GALILEAN TRANSFORMATIONS ECHOES FROM MOVING TARGETS DOPPLER-SHIFT VELOCIMETERS ACOUSTIC FIELDS NEAR CAUSTICS THE AIRY FUNCTION GENERALIZATION TO INHOMOGENEOUS MEDIA FIELD NEAR A TURNING POINT PHASE SHIFT AT A CAUSTIC SHADOW ZONES AND CREEPING WAVES POINT SOURCE ABOVE A LOCALLY REACTING SURFACE IN A STRATI?ED MEDIUM RESIDUES SERIES FOR THE SHADOW ZONE CREEPING WAVES RAY SHEDDING BY A CREEPING WAVE SOURCE OR LISTENER ON THE EDGE OF A WEDGE SOURCE ON EDGE LISTENER ON THE EDGE CONTOUR-INTEGRAL SOLUTION FOR DIFFRACTION BY A WEDGE METHOD OF IMAGES FOR INTEGER WEDGE INDEX GENERALIZATION TO NONINTEGER WEDGE INDICES GEOMETRICAL-ACOUSTIC AND DIFFRACTED-WAVE CONTRIBUTIONS FOR THE WEDGE PROBLEM THE GEOMETRICAL ACOUSTICS PORTION OF THE FIELD THE DIFFRACTED WAVE ASYMPTOTIC EXPRESSION FOR THE DIFFRACTED WAVE PHYSICAL INTERPRETATION OF THE DIFFRACTED WAVE APPLICATIONS OF WEDGE-DIFFRACTION THEORY INSERTION LOSS OF SINGLE-EDGED BARRIERS FAR FIELD OF A SOURCE ON THE SIDE OF A BUILDING BACKSCATTERING FROM AN EDGE EFFECTS OF VISCOSITY AND OTHER DISSIPATIVE PROCESSES THE NAVIER–STOKES–FOURIER MODEL THE STRESS TENSOR THE ENERGY EQUATION CONSTITUTIVE RELATIONS FOR A FLUID VALUES OF VISCOSITY AND THERMAL CONDUCTIVITY TRANSPORT PROPERTIES OF WATER LINEAR ACOUSTIC EQUATIONS AND ENERGY DISSIPATION LINEAR ACOUSTIC EQUATIONS THE ENERGY CONSERVATION-DISSIPATION COROLLARY ATTENUATION OF PLANE SOUND WAVES VORTICITY, ENTROPY, AND ACOUSTIC MODES DISPERSION RELATIONS FOR THE COMPONENT MODES A GENERALIZATION BASED ON THE SUPERPOSITION PRINCIPLE VORTICITY MODE ACOUSTIC MODE THE ENTROPY MODE ACOUSTIC BOUNDARY-LAYER THEORY BOUNDARY CONDITIONS AT A SOLID SURFACE VORTICITY- AND ENTROPY-MODE FIELDS NEAR A SOLID SURFACE BOUNDARY CONDITION ON THE ACOUSTIC-MODE FIELD ENERGY LOSS FROM THE ACOUSTIC MODE AT A BOUNDARY PLANE-WAVE RE?ECTION AT A SOLID SURFACE ATTENUATION AND DISPERSION IN DUCTS AND THIN TUBES PROPAGATION IN WIDE DUCTS PROPAGATION IN NARROW TUBES SLAB WITH CIRCULAR PORES VISCOSITY EFFECTS ON SOUND RADIATION REVISION OF THE KIRCHHOFF-HELMHOLTZ THEOREM TRANSVERSELY OSCILLATING RIGID BODIES STOKES FLOW LIMIT THIN-BOUNDARY-LAYER APPROXIMATION GUTIN’S PRINCIPLE HELICOPTER ROTOR NOISE RELAXATION PROCESSES PARTITIONING OF INTERNAL ENERGY THE BULK VISCOSITY INSTANTANEOUS ENTROPY FUNCTION FLUID-DYNAMIC EQUATIONS WITH RELAXATION LNCLUDED THE RELAXATION EQUATIONS NUMERICAL VALUES FOR THE CONSTANTS OF THE MODEL ABSORPTION OF SOUND LINEAR ACOUSTIC EQUATIONS FOR AIR ENERGY COROLLARY DISPERSION RELATION FOR PLANE TRAVELING WAVES ABSORPTION BY RELAXATION PROCESSES PHASE-VELOCITY CHANGES DUE TO RELAXATION PROCESSES NONLINEAR EFFECTS IN SOUND PROPAGATION NONLINEAR STEEPENING PLANE WAVES IN HOMOGENEOUS MEDIA STEEPENING OF WAVEFORMS GENERATION OF HARMONICS FOURIER-SERIES REPRESENTATION CONSERVATION OF ENERGY WEAK-SHOCK THEORY THE RANKINE–HUGONIOT RELATIONS WEAK SHOCKS THE EQUAL-AREA RULE N WAVES AND ANOMALOUS ENERGY DISSIPATION PLANE-WAVE PROPAGATION OF AN N WAVE DISSIPATION OF ACOUSTIC ENERGY EVOLUTION OF SAWTOOTH WAVEFORMS NONLINEAR DISSIPATIVE WAVES APPROXIMATE EQUATIONS FOR TRANSIENT PLANE WAVES MODI?CATION TO INCLUDE NONLINEAR EFFECTS THE BURGERS EQUATION RISE TIMES AND THICKNESSES OF WEAK SHOCKS RELAXATION EFFECTS ON SHOCK STRUCTURE TRANSITION TO OLD AGE REDUCTION TO THE LINEAR DIFFUSION EQUATION SOLUTION OF THE BOUNDARY-VALUE PROBLEM RELATIVE IMPORTANCES OF NONLINEAR AND DISSIPATIVE EFFECTS TRANSITION FROM SAWTOOTH TO OLD AGE NONLINEAR EFFECTS IN CONVERGING AND DIVERGING WAVES CORRECTED TRAVEL TIME ALONG RAY PATH ASYMPTOTIC FORM OF A TRANSIENT PULSE N WAVES IN INHOMOGENEOUS MEDIA: SPHERICAL WAVES N-WAVE PROPAGATION WAVES WITH SPHERICAL SPREADING BALLISTIC SHOCKS: SONIC BOOMS LINEAR ACOUSTIC MODEL FOR SOUND GENERATION BY A MOVING BODY GEOMETRICAL-ACOUSTICS INTERPRETATION NONLINEAR MODI?CATIONS