CONTENTS 



CHAPTER V 



MEMBRANES AND PLATES 



ABT. PAGE 



52. Equation of Motion of a Membrane. Energy . . . 139 



53. Square Membrane. Normal Modes . . . . . 142 



54. Circular Membrane. Normal Modes .'"''/ . . . 144 



55. Uniform Flexure of a Plate ...'.... 150 



56. Vibrations of a Plate. General Results . . k /. 152 



57. Vibrations of Curved Shells . 155 



CHAPTER VI 



PLANE WAVES OF SOUND 



58. Elasticity of Gases . . . ... . ,- . . 157 



59. Plane Waves. Velocity of Sound . -. . . . . 160 



60. Energy of Sound- Waves . . . ... ... 163 



61. Reflection . . . . 168 



62. Vibrations of a Column of Air . . . , . . 170 



63. Waves of Finite Amplitude . / ... . . 174 



64. Viscosity . . 183 



65. Effect of Heat Conduction . . . ; . . . . 187 



66. Damping of Waves in Narrow Tubes and Crevices . . 190 



CHAPTER VII 



GENERAL THEORY OF SOUND WAVES 



67. Definitions. Flux. Divergence 197 



68. Equations of Motion . 200 



69. Velocity-Potential 201 



70. General Equation of Sound Waves 204 



71. Spherical Waves 205 



72. Waves resulting from a given Initial Disturbance . . 212 



73. Sources of Sound. Reflection 214 



74. Refraction due to Variation of Temperature . . . 216 



75. Refraction by Wind 219 



CHAPTER VIII 



SIMPLE-HARMONIC WAVES. DIFFRACTION 



76. Spherical Waves. Point-Sources of Sound .... 223 



77. Vibrating Sphere 228 



78. Effect of a Local Periodic Force . 233 



