Index
‘Note: Page numbers followed by “f” indicate figures; “t” indicate tables and “b” indicate boxes.’
Absorption coefficients (room)
Eyring, 535–536
Sabine, 535–536
Absorption in air, 536
Acoustic, definition, 11
Acoustic components, 143–229
Acoustic generators, 107–112
Acoustic impedance, 16
Acoustic inertance, See
Mass
Acoustic radiation impedance, 821
Acoustic transformers, 155–161
Acoustical, definition, 12
Acoustical circuits, 102–112
Acoustical elements, 102–104
Acoustical holography, 713–715
Acoustical standards, 16
Acoustics
in concert halls, 547
in living rooms, 549–552
Adiabatic, definition, 7
Adiabatic alternations, 7–8
Admittances
conversion to impedance analogies, 124–125
definitions, 85
mechanical, 81–82
Air attenuation constant, 537t
Air density, 14–15
Air losses, 500–501
Air speed, 15–16
Air-suspension loudspeakers, 332
Airy
diffraction pattern, 628
disk, 637–639
stress function, 747–748
Alignment tables for loudspeaker in
bass-reflex enclosure, 374–376
Alternating signal voltage, 792–794
American Standards Assoc., 16
Analogies, 81–82
admittance type, 85
conversion of, 124–125
impedance type, 85
rotational, 112
transformation, 84
Angular eigenfrequency, 778
Arbitrary specific acoustic impedance, 732–734
Attenuation of sound in air, 536
Auditoriums
mean free path, 534
reverberation time, 535–536
sound absorption coefficients, 534
sound decay rate, 531–532
sound energy density, 17–18
sound pressure levels, 15
Average room absorption coefficient, 535
Axisymmetric solutions to shell wave equations, 754–755
Baffle
finite, 336–337
infinite, 336
open back, 337
unbaffled, 334–336
Barometric pressure (atmospheric), 14
Bass quality
explanation, 259
pressure-gradient microphone, 265
ribbon microphone, 263
Bending-wave velocity
in plate, 740
in shell, 749
Bends in horns, 496–498
of continuity at center, 755
slip, 207
of zero bending at perimeter, 755
of zero radial strain at perimeter, 755–756
Boundary integral method, 553–603
case study, 567–570
Boundary layer thickness, 213
Boundary value method, 553–603
Box
open-back, 337
Capacitor microphones
construction and properties, 249
humidity effects, 249
temperature effects, 248
Cardioid pattern, 239
hypercardioid, 263
supercardiod, 263
Cellphone acoustics, 445–462
call loudspeaker, 445
diaphragm, 445
electret microphone, 452–455
low-pass filter, 448–449
magnetic fields, 450
MEMS microphone, 455–457
sidetone, 460–461
turbulence, 450–451
wind noise, 451
Charles-Boyle gas law, 28
Circular membrane
See also
Rectangular membrane
Eigenfunctions, 729f
Green’s function for, 728–730
membrane wave equation solution for, 727–728
modes, 728
radiation from circular membrane without baffle, 731–739
boundary conditions, 731–732
far-field pressure, 738–739
radiation impedance, 737–738
simultaneous equations for power-series coefficients, 736–737
solution of free-space wave equation, 735–736
solution of membrane wave equation, 734–735
wave equation for membrane in free space, 732–734
Circular plate
modes of simply supported, 743–745
solution of plate wave equation for, 741–742
Clamped circular plate
eigenfunctions, 744f
eigenvalues for, 743t
modes of, 742–743
Closed tube, 55–58
See also
Tubes
Coefficients
absorption, 535–536
Coil, voice, 307–310
Coil driving force, 753–754
Coil impedance at perimeter, 756–757
Coil inductance, 772–773
Combination microphones, 262–265
Complex wavenumber of shell, 762
Compliance, 757
closed box, 337–366
closed tube, 207
drive unit, 278–279
jug, 148
mechanical, 89–91
series, acoustic, 146–149
Components, acoustic, 143–229
Condenser microphones, See
Capacitor microphones
Cone, See
Diaphragm
Conical horn, 474–477
Connector, exponential, 158–161
Constants
barometric pressure, 14
decay, room, 527
density-of-air, 15
drive unit, 279–280
flare, 483–484
reference quantities, 18–19
speed of sound, 15–16
Thiele-Small, 440
Continuity equation, 29–31
Coordinates
cylindrical, 70–73
rectangular, 68–69
spherical, 73–78
Coupled shell formulation, 764
Coupler, See
Connector
Cross-section shapes, horns, 498–499
Crossover networks, 436–440
Curvature of membrane, 722–723
Cut-off frequency of horn, 440–441
Cylindrical wave, 62–64
Decay curves, for sound in rooms, 531
Delay line ignoring stray capacitance, 807–808
Delay path length, 804–805
Density, air
definition, 15
formula, 15
normal, 15
variational, 15
Diameter, effective, of diaphragms, 310
Diaphragms
behavior, 310–314
diameter, effective, 310
Diffraction of plane wave
through resilient screen, 688–690
through rigid screen, 687–688
Diffuse sound field, 533
Dimensionless parameter, 764–765
Dipole source, See
Doublet
Dipole strength, 181
Direct sound, 547–548
Directivity, 189
Directivity characteristics
continuous delay, 795–801
discretization effects into rings of finite width, 802–803
far-field sound pressure, 810
neutralization of stray capacitances, 810–814
practical delay line, 804–810
Directivity factor, 189
Directivity index (DI)
calculation, 190–194
definition, 189
of sources, 192
dipole point source (doublet), 179–183
sphere (pulsating & oscillating), 164–167
Dirichlet boundary condition, 731
Dispersive medium, 741
Displacement, 747–748
of shell, 754
Distortion
horn, 472–474
large-amplitude waves, 478
loudspeakers, 322–325
phase delay of crossover, 435–436
transient, 322–323
Doublet
microphone, 179–183
piston without baffle, 184–185
simple, 182
Driving pressure, 732–734
Dual diaphragm microphones, 265–275
Dynamic loudspeaker
See Direct-radiator Loudspeakers
Dynamic membrane compliance, 818
Dynamic microphone, 241–248
Dynamic resistance, 818
Dynamic shell wave equations, 747–748
Early sound, 539–540
Eddy current, 772
Effective diameter of diaphragm, 310
Effective length of tube, 145
Effective particle velocity, 16
Effective sound pressure, 15
Effective volume velocity, 16
Efficiency
horn, 466–468
loudspeakers, 295–296
for 100-mm magnesium plate, 788t
for 25 mm aluminum shell, 768t
of shallow spherical shell with infinite load at perimeter, 761f
of shallow spherical shell with zero load at perimeter, 759f
of circular membrane, 729f
of clamped circular plate, 744f
of free circular plate, 747f
of rectangular membrane, 725f
of simply supported circular plate, 745f
Eigenvalues
calculation, 757–758
for clamped circular plate, 743t
with finite load at perimeter, 760
for free circular plate, 746t
with infinite load at perimeter, 760
for simply supported circular plate, 745t
with zero load at perimeter, 758–759
Electret microphone, 452–455
Electrical damping resistance, 779
Electrical impedance, 775–776
Electro-mechano-acoustical circuit, 814–815
Electrodynamic loudspeakers, 277–330
advantages, 277–278
constants, 247
construction, 278–280
design factors, 302–306
diaphragm, 310–314
directivity, 314–316
dual concentric, 440–441
efficiency, 295–296
element values, 289
impedance, input, 294
metals, 308t
non-linearity, 323–330
power output, 287–288
response, 292–293
transfer function, 316–318
transient, 318–323
unbaffled, 334–336
voice-coil velocity, 283–284
Electromagnetic microphones, 241–248
Electromechanical conversion factor, 732–734
directivity control, 794–795
lumped-element model of, 814–815
Electrostatic microphones, See
Capacitor Microphones
Elements of circuits
acoustical, 102–112
compliance, acoustic, 105–106
compliance, mechanical, 89–91
general, 81–82
generator, acoustic, 107–112
generator, mechanical, 92–93
mass, mechanical, 294
mechanical, 81–82
resistance, acoustic, 106–107
resistance, mechanical, 91–92
transformers, acoustic, 155–161
transformers, mechanical, 94
Elvamide, 792–794
Enclosures
closed-box, 337–366
End corrections, tubes, 144–145
Energy density, definition, 17–18
Energy flux, See
Intensity
Exponential connector, 158–161
Eyring, equation, 535–536
Far-field
of free plate with evenly distributed radiation load, 781–784
response of induction loudspeaker, 784–789
sound pressure, 810
directivity patterns at various frequencies, 811f
parameters for idealized electrostatic loudspeaker and delay line, 812t
Ferrofluid, 326
Field, sound
near, 183–184
diffuse, 533
direct, 536
far, 183–184
Figure-of-eight directivity pattern, 794–795
Finite element modal (FEM), 738–739
Flare constant, 483–484
Fluctuations of sound, in room, 533
Fluid–structure coupling, 731
Fluid–structure interaction, 721
Flux density
definition, 485–486
Force equation, 25
Force transmission coefficient, 737
Fourier’s law, 149
Fraunhofer
diffraction pattern, 628
diffraction zone, 631–633
Free circular plate
Eigenfunctions of, 747f
Eigenvalues for, 746t
modes of, 746–747
Free-space wave equation
membrane in, 732–734
Fresnel region, 631–633
Friction, in air, 145
Fundamental in vacuo resonance frequency, 738–739
Fundamental resonance, 757
Gas
adiabatic, 7
isothermal, 7
Generators
acoustic, 107–112
loudspeakers
See Direct radiator Loudspeakers
mechanical, 92–93
Graphite, 792–794
for circular membrane, 728–730
for rectangular membrane, 724–726
for shallow spherical shell, 749–752
Handsfree loudspeaker, 445–446
Hankel functions, 727
Harmonic function, 748–749
Helmholtz form, 748–749
cylindrical coordinates, 70–73
infinite lossy tube, 213–214
inhomogeneous, 609
plane wave, 37
rectangular coordinates, 68–69
for sound pressure waves, 723
spherical coordinates, 73–78
History, 1–5
Homogeneous membrane wave equation, 724–725
Homogeneous wave equation in coordinate system, 740
Homogenous wave equation, 857
Horn drive units, 463–464
circuit for, 464–465
efficiency, 466–468
response, 468–472
Horn loudspeakers, 463–510
Horns
advantages, 463
bends, 496–498
circuit for, 464–465
conductance, 466
cross-section shapes, 498–499
disadvantages, 463
finite, 487–496
flare constant, 483–484
frequency response, 468–472
high frequencies, 471–472
Klipsch, 502
low-frequency, 469–471
materials, 499–509
midfrequency, 469
mouth, 477
Humidity, effects, 241
Huygens-Fresnel principle, 605–606
Hyperbolic Bessel function, 741–742
Impedances
acoustic, 16
closed box, 337–366
definitions, 16–17
horn, See
Horns
infinite, 48–49
loudspeaker, 309–310
measurement, 47–48
perforated sheet, 154–155
screens, 149
transducer, 127–140
tubes, 43–60
Indium-tin-oxide (ITO), 792–794
analogous circuit, 772–776
boundary conditions, 777–781
coil and suspension parameters, 785t
construction, 770–772
electro-mechano-acoustical analogous circuit, 772f
far-field pressure of free plate with evenly distributed radiation load, 781–784
far-field response, 784–789
radiation from circular plate in infinite baffle, 770
Inertance, See
Mass
Inhomogeneous membrane equation, 724–725
Inhomogeneous wave equation, 858
Intensity
definition, 17
level, 19–20
Isothermal, definition, 7
Jug, 147
Kelvin function, See
Thomson function
Kirchhoff-Helmholtz boundary integral, 609–611
Klipsch horn, 502
Knudsen number, 151
cylindrical coordinates, 70–73
Green’s theorem, 609–610
rectangular coordinates, 68–69
spherical coordinates, 73–78
Large amplitude waves, 478
Least-mean-squares method, 663–664
Legendre function, 76
Levels, 17–22
Levers, 94–102
Loudness
concert hall, 547
listening room, 549–552
Loudspeakers
bass-reflex enclosed, 374–376
box enclosed, 337–366
direct radiator, See
Electrodynamic loudspeakers
dual concentric, 440–441
electrodynamic, 277–278
magnet size, 303–306
wave, 357–360
Lumped-element model of electrostatic loudspeaker
dynamic membrane compliance and dynamic resistance, 818
electro-mechano-acoustical circuit, 814–815
frequency response, 820–826
negative compliance and stability, 815–816
radiation impedance, 819–820
setting tension to limiting displacement and maintaining stability, 818–819
static membrane compliance, 816–818
Magnesium alloy, 784–786
Magnet size, 303–306
Magnetic fields, 450
Mass
acoustic, 144
diaphragm, 310–314
mechanical, 81–82
voice-coil, 307–310
Mass loading factor, 757
Materials, sound absorbent, 347–349
Matrices
Mean free path
of waves, 534
Mechanical circuits, 81–82
Mechanical compliance, 89–91
Mechanical elements, 85–102
Mechanical generators, 92–93
Mechanical resistance, 91–92
Mechano-acoustic transducers, 120–121
Membrane(s), 721
Green’s function for circular membrane, 728–730
Green’s function for rectangular membrane, 724–726
modes of circular membrane, 728
modes of rectangular membrane, 724
radiation from circular membrane without baffle, 731–739
and stator mass control, 825–826
stiffness control, 821
vibroacoustics, 721
wave equation
in polar coordinates, 727
in rectangular coordinates, 721–723
solution, 734–735
solution for circular membrane, 727–728
solution for rectangular coordinates, 723–724
MEMS microphone, 455–457
Metals
density, 308t
resistivity, 308t
Microphones, 231–275
capacitor, See
Capacitor microphones
dual diaphragm, 265–275
electret, 452–455
electrostatic, See
Capacitor microphones
MEMS, 455–457
moving coil, 241–248
piezoelectric, 115
ribbon, See
Ribbon microphones
summary, 231t
Modified Walker’s equation, 738–739
Mutual impedance of
bend in horn, 496–498
pistons in closed box with or without lining, 349–352
Negative impedance, 732–734
Neumann functions, 727
Neutral layer, 740
Neutralization of stray capacitances, 810–814
constant impedance delay line, 812f
Non-linear distortion
in horns, 474
in loudspeakers, 474
Normal frequency diagram, 532f
On-axis pressure, 738–739
Orchestra power levels, 544
Oscillating sphere, 196–197
Pipes, junctions, 158–161
Piston
without baffle, 676
directivity, 705–706
eigenfrequency, 759
Plane waves
impedance terminated tube, 43–44
reflection from plane, 162–164
modes
of clamped circular plate, 742–743
of free circular plate, 746–747
of simply supported circular plate, 743–745
solution of plate wave equation for circular plate, 741–742
wave equation in polar coordinates, 740–741
Point source
dipole (doublet), 179–183
monopole (simple), 168
Poisseulle flow, 224
Poisson’s ratio, 740
Polar coordinates
membrane wave equation in, 727
plate wave equation in, 740–741
shell wave equation in, 747–749
Polar diagram, See
Directivity patterns
Polyester, 792–794
Polyimide, 792–794
Port
definition, 374–376
performance, 390
Power
Prandtl number, 209–210
Pressure
ambient (atmosphere), 10–11
reference, 19
Pressure level, 310–311
Pressure spectrum level, 22
Product theorem, 700f
Propagation
through gas, 8–10
general, 11–13
in porous materials, 347–348
speed in air, 10
Pulsating sphere, 196
of loudspeakers, 278–279
of perforated sheet, 155
Radial membrane force, 756–757
Radiation
from concave dome in infinite baffle, 594–602
from convex dome in infinite baffle, 588–594
from dipole point source (doublet), 179–183
from infinite cylinder or line source, 554–555
from infinite strip in infinite baffle, 691–695
from linear array (beam-forming), 171–173
from loudspeaker, 636
mass control, 823–824
from monopole point source (simple), 168
from piston in a sphere, 582–588
from piston in finite circular closed baffle, 676–683
from piston in finite circular open baffle, 659–674
from piston in infinite baffle, 198–201
from point source on sphere, 567–570
from rectangular cap in a sphere, 577–582
from rectangular piston in infinite baffle, 701–703
from resilient disk in infinite baffle, 647–657
from resilient disk without baffle, 636–647
resistance control, 824
from spherical cap in a sphere, 570–577
Rate of sound decay, 527
Rayl, 16
Rayleigh distance, 633
Rayleigh integrals, 606–608
Reactance, See
Impedance
Receiver, 446–448
Rectangular coordinates, membrane wave equation in, 721–723
Rectangular membrane
See also
Circular membrane
Eigenfuctions of, 725f
Green’s function for, 724–726
modes, 724
Reference
intensity, 19–20
power, 22
Reflection
plane wave from plane, 162–164
plane wave from plane resilient object, 686–687
plane wave from plane rigid object, 684–686
point source from plane, 623–625
Relative humidity, See
Humidity
Resistance
frictional, 91
lossy tube, 220
mechanical, 91–92
radiation, oscillating sphere, 192
radiation, pistons, 625–635
radiation, pulsating sphere, 167
screens, 150
viscous, 91
voice-coil, 341–342
Resistivity
metals, 308t
wire, 768
Resonance curve, 526–527
Response of loudspeaker
in bass-reflex enclosure, 374–376
in closed-box enclosure, 337–366
in infinite baffle, 336
Reverberant sound, 539–541
definition, 539
enclosures, 533–535
living rooms, 549
optimum, 538
Reynolds number, 450
Ribbon microphones, 259
Sabine absorption coefficient, 860
Scattering
plane wave from sphere, 555
point source from sphere, 560–566
Shallow spherical shell
green’s function for, 749–752
Shear force, 756–757
Sheets, perforated, 154–155
Shell(s), 747–749
aluminum shell parameters, 767t
coil and suspension parameters, 768t
eigenfrequencies for aluminum shell, 768t
green’s function for shallow spherical shell, 749–752
mass, 768–769
radiation from circular shallow spherical shell, 752–769
solution of wave equation for shell, 762
wave equation in polar coordinates, 747–749
Simple source, 168
Single steady-state homogeneous wave equation, 748–749
Slit, impedance, 151
Sound
definition, 5–8
direct, 540–541
energy density, 17–18
intensity, 17
reverberant, 540–541
speed, 6
weighting curves, 21f
Sound absorption, in air, 534
Sound energy, density, 17–18
Sound levels, 21
for music, 542–544
for speech, 542–544
Sound strength, G, 539
Sources
dipole point source (doublet), 179–183
linear array (beam-forming), 171–173
monopole point source (simple), 168
rooms, inside, 548
spherical
See Spherical sources
two (simple) point sources in phase, 168–170
Specific acoustic impedance
cylindrical wave, 61–62
definition, 16–17
plane wave, 53–54
spherical wave, 63–64
Specific diaphragm impedance, 737–738
Specific heat, of air, 7
Spherical wave, 65–67
Squawker, 425
Static membrane compliance, 816–818
Stator resistance control, 821–823
Stiffness (reciprocal of compliance), See
Compliance
Stray capacitances
delay line ignoring, 807–808
neutralization of, 810–814
Superposition, 95–96
of waves, 533
Terminology, 11
Thermal and viscous losses, 207
Thermal conductivity, 209
Thermal diffusion wave, 28
Thévenin’s theorem, 125–127
Thiele-Small
measurement, 297–300
Thomson function, 749
Time reversal, 715–717
Transducers, 113
Transformers, acoustic, 155–161
Transient behavior
loudspeakers, 318–323
rooms, 527–530
Transmission
matrix, 813–814
Tubes
closed, 55–58
filled with absorbent material, 60–61
intermediate diameter, 153–154
lossy, 207–229
piston in end of, 109
specific acoustic impedance, 66–67
Turbulence, 450–451
Units, mks, SI, 305–306
Velocity distribution, 762–763
Vibroacoustics, 721
induction loudspeakers, 770–789
membranes, 721
plates, 740–741
shells, 747–749
Viscous and thermal losses, 207
Voice-coil
design, 307–310
velocity, 283–286
Volume velocity, 16
Wave equation for membrane in free space, 732–734
See also
Helmholtz wave equation
Wavelength, 10
Waves
backward traveling, 514–516
cylindrical, 62–64
forward traveling, 514–516
free progressive, 17
plane, 555
spherical, 65–67
standing, stationary, 511–512
Weighting curves, 21f
Wind noise, 451
Wire mass, 768–769
Young’s modulus, cone, 327
Zero shear force, 746
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