Physics in the Arts

Cover Page......Page 1
Title Page\n......Page 4
Copyright Page......Page 5
Light and Sound......Page 12
Table of Contents......Page 6
1 Light and Light Waves......Page 16
1.1 Speed of Light......Page 20
1.2 Electromagnetic Spectrum......Page 21
1.3 Polarization......Page 22
2.1 Specular Reflection of Light......Page 25
2.2 Refraction of Light......Page 29
2.3 Total Internal Reflection......Page 32
2.4 Reflection and Refraction in Diamonds......Page 36
2.5 The Rainbow......Page 40
2.6 Questions......Page 42
3.1 The Prism......Page 45
3.2 Converging and Diverging Lenses......Page 46
3.3 Focal Length......Page 48
3.4 Images—Real and Virtual......Page 51
3.5 Three Easy Rays......Page 54
3.6 The Lens Formula......Page 56
3.6.1 Note on Magnification......Page 60
3.7 Lens Aberrations......Page 62
3.7.1 Chromatic Aberrations......Page 63
3.7.2 Spherical Aberration......Page 64
3.8 Questions......Page 67
4 The Eye......Page 71
4.1 Accommodation......Page 73
4.2 Eyeglasses......Page 75
4.3 Nearsighted Eye......Page 76
4.5 Astigmatic Eye......Page 77
5.1 The Camera......Page 78
5.2 Focusing the Camera......Page 79
5.3 Choosing the Exposure Time......Page 82
5.4 Choosing the Aperture......Page 83
5.5 Depth of Field......Page 84
5.5.1 Why the f Number?......Page 85
5.6 The Film......Page 86
5.7 Digital Photography......Page 90
5.8 Putting it All Together: Taking a Photograph......Page 91
5.9 Questions......Page 95
6.1 Color......Page 97
6.2 Color Sensitivity of the Eye......Page 99
6.3 Physical and Psychological Color......Page 104
6.4 Color: Hue, Saturation, and Brightness......Page 105
6.6 Scattering or Diffuse Reflection......Page 107
6.7 Questions......Page 113
7.1 Primary Colors......Page 114
7.2 Adding Primary Colors......Page 115
7.3 The Color Triangle......Page 118
7.5 Spectral Colors......Page 122
7.6 Non-Spectral Colors......Page 127
7.7 Summary......Page 128
7.8 Additive Color Mixing in Painting......Page 129
7.9 Questions......Page 132
8.1 Filters......Page 133
8.2 Subtractive Primary Colors......Page 135
8.2.1 Subtractive primaries......Page 137
8.3 Color Photography......Page 139
8.4 Pigments......Page 140
8.5 Change in Saturation......Page 143
8.6 Why Do Blue and Yellow Make Green?......Page 145
8.7 Change in Hue......Page 146
8.8 Questions......Page 149
9.2 Pigments......Page 151
9.3 Structural Color: Iridescence......Page 152
9.4 More Color-Generating Mechanisms Due to Iridescence......Page 154
9.5 Color in Gemstones......Page 157
9.7 Mineral Color Due to Color Centers......Page 159
9.8 Color in Gems Due to Band Gap Absorption of Light......Page 160
10 Periodic Oscillations......Page 163
10.1 Displacement Graph: Position x Changes with Time t......Page 166
10.2 The Period T and the Frequency f......Page 168
10.4 Speed of Motion......Page 169
10.5 Questions......Page 171
11 Simple Harmonic Motion......Page 173
11.1 The Spring Constant......Page 175
11.2 Oscillation Frequency for Simple Harmonic Motion (SHM)......Page 176
11.3 Wave Shape of Simple Harmonic Motion......Page 178
11.4 Phase Angle......Page 180
11.5 Questions......Page 181
12.1 Damped Oscillations—The Concept of “Damping Time”......Page 183
12.2 Resonance......Page 185
12.4.1 Resonators in Musical Instruments......Page 190
12.5 Questions......Page 192
13.1 Principle of Superposition......Page 194
13.2.1 Two Pure Tones of the Same Frequency......Page 195
13.3 Beats......Page 197
13.4 Harmony......Page 199
13.5 For the Fun of it: Lissajous Figures......Page 200
13.6 Questions......Page 203
14.1 Propagation of a Pulse......Page 205
14.2 Longitudinal and Transverse Waves......Page 207
14.3 Sound Waves in Air are Longitudinal Waves......Page 208
14.4 Speed of Sound in Air......Page 210
14.5 Wavelength and Frequency......Page 211
14.5.1 Relevance to Size of Instruments or Loudspeakers......Page 212
14.6 Sound Propagation......Page 213
14.7 Interference of Sound Waves......Page 214
14.8 Concert Hall Acoustics......Page 216
14.9 Questions......Page 220
15 Sound Perception: Pitch, Loudness, and Timbre......Page 221
15.1 Loudness and Amplitude......Page 222
15.2 Loudness and Frequency......Page 225
15.3 Pitch Discrimination......Page 228
16.1 The Parts of the Ear......Page 229
16.2 Place Theory of Pitch Perception......Page 231
16.3 What Do the Auditory Nerves Tell the Brain?......Page 232
17.1 Single Modes......Page 235
17.2 Higher Modes......Page 237
17.3 Traveling Versus Standing Waves......Page 238
17.4 The Voicing Formula......Page 240
17.5 How Do Modes Relate to Music?......Page 241
17.7 Plucked Strings: Missing Partials......Page 242
17.9 Real Strings Have Some Stiffness......Page 243
17.10 Questions......Page 244
18.1 Pressure Pulse in a Pipe......Page 246
18.3 Standing Waves in Open Pipes......Page 248
18.4 Fundamental Frequency of Open Pipe......Page 249
18.5 Higher Modes of Open Pipe......Page 250
18.6 Fundamental Mode of Closed Pipe......Page 252
18.7 Higher Modes of Closed Pipe......Page 253
18.9 Other Shapes......Page 255
18.11 Questions......Page 256
19.1 The Fourier Theorem......Page 258
19.2 Sound Spectrum......Page 259
19.3 Fourier Analyzer (Sound Analyzer)......Page 264
19.4 Fourier Synthesis......Page 266
19.5 Why Can’t We Synthesize a Stradivari?......Page 267
19.6 Questions......Page 269
20 Musical Scales......Page 271
20.1 Musical Intervals......Page 272
20.2 Consonance (Harmony): Simple Number Ratios......Page 273
20.3 The Major Triad......Page 274
20.4 Constructing a Scale: The Just Scale......Page 275
20.5 Whole and Half Tone Intervals......Page 278
20.6 Names of Intervals......Page 279
20.7 Transposing: Why Black Keys?......Page 281
20.8 Perfection Sacrificed: The Tempered Scale......Page 282
20.10 The Natural Scale......Page 288
20.11 Questions......Page 289
21.1 Structure of Musical Instruments......Page 290
21.2 Excitation Mechanism......Page 291
21.3 Playing a Tune......Page 293
21.4 Questions......Page 298
22 Solutions to Problems......Page 299
Index......Page 322