Physics in the Arts (eBook)

Front Cover 1
Physics in the Arts 4
Copyright Page 5
Table of Contents 6
Introduction 12
Chapter 1. Light and Light Waves 16
1.1 Speed of Light 20
1.2 Electromagnetic Spectrum 21
1.3 Polarization 22
Chapter 2. Reflection and Refraction 25
2.1 Specular Reflection of Light 25
2.2 Refraction of Light 29
2.3 Total Internal Reflection 32
2.4 Reflection and Refraction in Diamonds 36
2.5 The Rainbow 40
2.6 Questions 42
Chapter 3. Lenses 45
3.1 The Prism 45
3.2 Converging and Diverging Lenses 46
3.3 Focal Length 48
3.4 Images—Real and Virtual 51
3.5 Three Easy Rays 54
3.6 The Lens Formula 56
3.7 Lens Aberrations 62
3.8 Questions 67
Chapter 4. The Eye 71
4.1 Accommodation 73
4.2 Eyeglasses 75
4.3 Nearsighted Eye 76
4.4 Farsighted Eye 77
4.5 Astigmatic Eye 77
Chapter 5. Photography 78
5.1 The Camera 78
5.2 Focusing the Camera 79
5.3 Choosing the Exposure Time 82
5.4 Choosing the Aperture 83
5.5 Depth of Field 84
5.6 The Film 86
5.7 Digital Photography 90
5.8 Putting it All Together: Taking a Photograph 91
5.9 Questions 95
Chapter 6. Color and Color Vision 97
6.1 Color 97
6.2 Color Sensitivity of the Eye 99
6.3 Physical and Psychological Color 104
6.4 Color: Hue, Saturation, and Brightness 105
6.5 Light Interaction with other Objects 107
6.6 Scattering or Diffuse Reflection 107
6.7 Questions 113
Chapter 7. Additive Color Mixing 114
7.1 Primary Colors 114
7.2 Adding Primary Colors 115
7.3 The Color Triangle 118
7.4 Low-Intensity Colors 122
7.5 Spectral Colors 122
7.6 Non-Spectral Colors 127
7.7 Summary 128
7.8 Additive Color Mixing in Painting 129
7.9 Questions 132
Chapter 8. Subtractive Color Mixing 133
8.1 Filters 133
8.2 Subtractive Primary Colors 135
8.3 Color Photography 139
8.4 Pigments 140
8.5 Change in Saturation 143
8.6 Why Do Blue and Yellow Make Green? 145
8.7 Change in Hue 146
8.8 Questions 149
Chapter 9. Color-Generating Mechanisms 151
9.1 Illuminating Light 151
9.2 Pigments 151
9.3 Structural Color: Iridescence 152
9.4 More Color-Generating Mechanisms Due to Iridescence 154
9.5 Color in Gemstones 157
9.6 Mineral Color Due to Charge Transfer 159
9.7 Mineral Color Due to Color Centers 159
9.8 Color in Gems Due to Band Gap Absorption of Light 160
Chapter 10. Periodic Oscillations 163
10.1 Displacement Graph: Position x Changes with Time t 166
10.2 The Period T and the Frequency f 168
10.3 Large and Small Numbers 169
10.4 Speed of Motion 169
10.5 Questions 171
Chapter 11. Simple Harmonic Motion 173
11.1 The Spring Constant 175
11.2 Oscillation Frequency for Simple Harmonic Motion (SHM) 176
11.3 Wave Shape of Simple Harmonic Motion 178
11.4 Phase Angle 180
11.5 Questions 181
Chapter 12. Damped Oscillations and Resonance 183
12.1 Damped Oscillations—The Concept of “Damping Time” 183
12.2 Resonance 185
12.3 Build-up Decay of Musical Tones 190
12.4 Applications in Music 190
12.5 Questions 192
Chapter 13. Adding Sound Sources: Beats and Harmony 194
13.1 Principle of Superposition 194
13.2 Three Special Cases 195
13.3 Beats 197
13.4 Harmony 199
13.5 For the Fun of it: Lissajous Figures 200
13.6 Questions 203
Chapter 14. Sound Waves 205
14.1 Propagation of a Pulse 205
14.2 Longitudinal and Transverse Waves 207
14.3 Sound Waves in Air are Longitudinal Waves 208
14.4 Speed of Sound in Air 210
14.5 Wavelength and Frequency 211
14.6 Sound Propagation 213
14.7 Interference of Sound Waves 214
14.8 Concert Hall Acoustics 216
14.9 Questions 220
Chapter 15. Sound Perception: Pitch, Loudness, and Timbre 221
15.1 Loudness and Amplitude 222
15.2 Loudness and Frequency 225
15.3 Pitch Discrimination 228
Chapter 16. The Ear 229
16.1 The Parts of the Ear 229
16.2 Place Theory of Pitch Perception 231
16.3 What Do the Auditory Nerves Tell the Brain? 232
Chapter 17. Vibration of Strings 235
17.1 Single Modes 235
17.2 Higher Modes 237
17.3 Traveling Versus Standing Waves 238
17.4 The Voicing Formula 240
17.5 How Do Modes Relate to Music? 241
17.6 Damping of Higher Partials 242
17.7 Plucked Strings: Missing Partials 242
17.8 Playing Harmonics 243
17.9 Real Strings Have Some Stiffness 243
17.10 Questions 244
Chapter 18. Pipes 246
18.1 Pressure Pulse in a Pipe 246
18.2 Reflections in Open and Closed Pipes 247
18.3 Standing Waves in Open Pipes 248
18.4 Fundamental Frequency of Open Pipe 249
18.5 Higher Modes of Open Pipe 250
18.6 Fundamental Mode of Closed Pipe 252
18.7 Higher Modes of Closed Pipe 253
18.8 Playing Tunes on Wind Instruments: Fingerholes and Overblowing 255
18.9 Other Shapes 255
18.10 Acoustic Length 256
18.11 Questions 256
Chapter 19. Fourier Analysis 258
19.1 The Fourier Theorem 258
19.2 Sound Spectrum 259
19.3 Fourier Analyzer (Sound Analyzer) 264
19.4 Fourier Synthesis 266
19.5 Why Can’t We Synthesize a Stradivari? 267
19.6 Questions 269
Chapter 20. Musical Scales 271
20.1 Musical Intervals 272
20.2 Consonance (Harmony): Simple Number Ratios 273
20.3 The Major Triad 274
20.4 Constructing a Scale: The Just Scale 275
20.5 Whole and Half Tone Intervals 278
20.6 Names of Intervals 279
20.7 Transposing: Why Black Keys? 281
20.8 Perfection Sacrificed: The Tempered Scale 282
20.9 Major and Minor Scales 288
20.10 The Natural Scale 288
20.11 Questions 289
Chapter 21. Musical Instruments 290
21.1 Structure of Musical Instruments 290
21.2 Excitation Mechanism 291
21.3 Playing a Tune 293
21.4 Questions 298
Chapter 22. Solutions to Problems 299
Chapter 2 299
Chapter 3 303
Chapter 5 307
Chapter 6 309
Chapter 7 309
Chapter 8 311
Chapter 10 316
Chapter 11 317
Chapter 12 317
Chapter 13 317
Chapter 14 317
Chapter 17 318
Chapter 18 318
Chapter 19 320
Chapter 20 321
Chapter 21 321
Index 322