Physics in the Arts

327 Pages·2008·5.533 MB·English

by  P.U.P.A. Gilbert, Willy Haeberli

Physics in the Arts
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Physics in the Arts
P.U.P.A. Gilbert
University of Wisconsin-Madison
and
W. Haeberli
University of Wisconsin-Madison
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Physics in the Arts
P.U.P.A. Gilbert and
Willy Haeberli
University of
Wisconsin-Madison
Contents
Introduction xi
LightandSound.................................................. xi
1 Light and Light Waves 01
1.1 SpeedofLight.......................................... 05
1.2 ElectromagneticSpectrum............................... 06
1.3 Polarization............................................ 07
2 Reflection and Refraction 10
2.1 SpecularReflectionofLight............................. 10
2.2 RefractionofLight...................................... 14
2.3 TotalInternalReflection................................. 17
2.4 ReflectionandRefractioninDiamonds ................... 21
2.5 TheRainbow........................................... 25
2.6 Questions.............................................. 27
v
vi Contents
3 Lenses 30
3.1 ThePrism.............................................. 30
3.2 ConvergingandDivergingLenses........................ 31
3.3 FocalLength........................................... 33
3.4 Images—RealandVirtual............................... 36
3.5 ThreeEasyRays........................................ 39
3.6 TheLensFormula...................................... 41
3.6.1 NoteonMagnification ............................ 45
3.7 LensAberrations....................................... 47
3.7.1 ChromaticAberrations............................ 48
3.7.2 SphericalAberration.............................. 49
3.8 Questions.............................................. 52
4 The Eye 56
4.1 Accommodation........................................ 58
4.2 Eyeglasses............................................. 60
4.3 NearsightedEye........................................ 61
4.4 FarsightedEye ......................................... 62
4.5 AstigmaticEye......................................... 62
5 Photography 63
5.1 TheCamera............................................ 63
5.2 FocusingtheCamera.................................... 64
5.3 ChoosingtheExposureTime............................. 67
5.4 ChoosingtheAperture.................................. 68
5.5 DepthofField.......................................... 69
5.5.1 WhythefNumber?............................... 70
5.6 TheFilm............................................... 71
5.7 DigitalPhotography..................................... 75
5.8 PuttingitAllTogether:TakingaPhotograph............... 76
5.9 Questions.............................................. 80
6 Color and Color Vision 82
6.1 Color.................................................. 82
6.2 ColorSensitivityoftheEye.............................. 84
6.3 PhysicalandPsychologicalColor ........................ 89
Contents vii
6.4 Color:Hue,Saturation,andBrightness.................... 90
6.5 LightInteractionwithotherObjects ...................... 92
6.6 ScatteringorDiffuseReflection.......................... 92
6.7 Questions.............................................. 98
7 Additive Color Mixing 99
7.1 PrimaryColors......................................... 99
7.2 AddingPrimaryColors.................................. 100
7.3 TheColorTriangle...................................... 103
7.4 Low-IntensityColors.................................... 107
7.5 SpectralColors......................................... 107
7.6 Non-SpectralColors.................................... 112
7.7 Summary.............................................. 113
7.8 AdditiveColorMixinginPainting........................ 114
7.9 Questions.............................................. 117
8 Subtractive Color Mixing 118
8.1 Filters................................................. 118
8.2 SubtractivePrimaryColors.............................. 120
8.2.1 Subtractiveprimaries.............................. 122
8.3 ColorPhotography...................................... 124
8.4 Pigments............................................... 125
8.5 ChangeinSaturation.................................... 128
8.6 WhyDoBlueandYellowMakeGreen?................... 130
8.7 ChangeinHue ......................................... 131
8.8 Questions.............................................. 134
9 Color-Generating Mechanisms 136
9.1 IlluminatingLight...................................... 136
9.2 Pigments............................................... 136
9.3 StructuralColor:Iridescence............................. 137
9.4 MoreColor-GeneratingMechanismsDuetoIridescence.... 139
9.5 ColorinGemstones..................................... 142
9.6 MineralColorDuetoChargeTransfer.................... 144
9.7 MineralColorDuetoColorCenters...................... 144
9.8 ColorinGemsDuetoBandGapAbsorptionofLight....... 145
viii Contents
10 Periodic Oscillations 148
10.1 DisplacementGraph:PositionxChangeswithTimet ...... 151
10.2 ThePeriodTandtheFrequencyf ........................ 153
10.3 LargeandSmallNumbers............................... 154
10.4 SpeedofMotion........................................ 154
10.5 Questions.............................................. 156
11 Simple Harmonic Motion 158
11.1 TheSpringConstant.................................... 160
11.2 OscillationFrequencyforSimpleHarmonicMotion(SHM). 161
11.3 WaveShapeofSimpleHarmonicMotion.................. 163
11.4 PhaseAngle............................................ 165
11.5 Questions.............................................. 166
12 Damped Oscillations and Resonance 168
12.1 DampedOscillations—TheConceptof“DampingTime”... 168
12.2 Resonance............................................. 170
12.3 Build-upDecayofMusicalTones........................ 175
12.4 ApplicationsinMusic................................... 175
12.4.1 ResonatorsinMusicalInstruments .................. 175
12.5 Questions.............................................. 177
13 Adding Sound Sources: Beats and Harmony 179
13.1 PrincipleofSuperposition............................... 179
13.2 ThreeSpecialCases..................................... 180
13.2.1 TwoPureTonesoftheSameFrequency.............. 180
13.3 Beats.................................................. 182
13.4 Harmony............................................... 184
13.5 FortheFunofIt:LissajousFigures....................... 185
13.6 Questions.............................................. 188
14 Sound Waves 190
14.1 PropagationofaPulse................................... 190
14.2 LongitudinalandTransverseWaves....................... 192
14.3 SoundWavesinAirAreLongitudinalWaves.............. 193
14.4 SpeedofSoundinAir................................... 195
Contents ix
14.5 WavelengthandFrequency .............................. 196
14.5.1 RelevancetoSizeofInstrumentsorLoudspeakers...... 197
14.6 SoundPropagation...................................... 198
14.7 InterferenceofSoundWaves............................. 199
14.8 ConcertHallAcoustics.................................. 201
14.9 Questions.............................................. 205
15 Sound Perception: Pitch, Loudness, and Timbre 206
15.1 LoudnessandAmplitude................................ 207
15.2 LoudnessandFrequency ................................ 210
15.3 PitchDiscrimination.................................... 213
16 The Ear 214
16.1 ThePartsoftheEar..................................... 214
16.2 PlaceTheoryofPitchPerception......................... 216
16.3 WhatDotheAuditoryNervesTelltheBrain?.............. 217
17 Vibration of Strings 220
17.1 SingleModes........................................... 220
17.2 HigherModes.......................................... 222
17.3 TravelingVersusStandingWaves......................... 223
17.4 TheVoicingFormula.................................... 225
17.5 HowDoModesRelatetoMusic?......................... 226
17.6 DampingofHigherPartials.............................. 227
17.7 PluckedStrings:MissingPartials......................... 227
17.8 PlayingHarmonics...................................... 228
17.9 RealStringsHaveSomeStiffness ........................ 228
17.10 Questions.............................................. 229
18 Pipes 231
18.1 PressurePulseinaPipe................................. 231
18.2 ReflectionsinOpenandClosedPipes..................... 232
18.2.1 BoundaryConditions ............................. 233
18.3 StandingWavesinOpenPipes........................... 233
18.4 FundamentalFrequencyofOpenPipe..................... 234
18.5 HigherModesofOpenPipe ............................. 235
18.6 FundamentalModeofClosedPipe ....................... 237