302 



INDEX 



[The numerals refer to the pages'] 



Forced oscillations, 16, 20, 47 

 effect of friction on, 28, 57, 104 



Fork, tuning, 132 



Fourier's theorem, 87, 92 



influence of discontinuities in, 92 

 law of convergence of coefficients in, 

 94 



Freedom, degrees of, 12, 34 



Free- free bar, transverse vibrations of 

 a, 124 



Free oscillations, 12 

 with friction, 24 

 general theory of, 44 



Frequency, range of, for audibility, 3 



Friction. See Dissipation 



Gas, elasticity of a, 159 



isothermal and adiabatic lines of a, 



157, 158 

 Graphical solution of period-equations, 



83, 125, 126, 128, 256, 258 

 Grating, transmission of sound by a, 



247 



Harmonic analysis, 101 

 Harmonics, 5 



Heat, vibrations caused by, 278 

 Heat-conduction, effect of, on sound 



waves, 187 



Hooke's law of elasticity, 11, 110 

 Huygens' principle, 249 



Imaginaries, use of, 53 



Impact, vibrations of a string due to, 



73, 99 



Indicator diagram, 157 

 Inertia, coefficients of, 42 

 ' Irrotational ' motion defined, 203 

 Interference of simple-harmonic vibra- 

 tions, 23 



of pure tones, 287 

 Intervals, musical, 5, 288 



degree of definition of, 297 

 Isothermal lines, 157 



Laplace's equation, 205 



Leslie's experiment, 237 



Lines of motion, 229 



Lissajous' figures, 49 



Loaded string, normal modes of a, 36, 



37,82 

 Local periodic force, effect of, in a 



gaseous medium, 233 

 Longitudinal vibrations, of bars, 

 114 



of columns of air, 170, 266 

 Loops, on a vibrating string, 70 



in a pipe, 171 



Membrane, transverse vibrations of a, 

 139 



normal modes of a rectangular, 

 142 



of a circular, 144 

 Mersenne's laws, 70 

 'Modulus of decay,' defined, 25 



of air-waves, 185 



of a vibrating sphere, 233 



of a resonator, 265 



of a pipe, 270 

 Modulus, Young's, 111 

 Multiple system, equations of motion 

 of a, 41, 44 



normal modes of a, 44 



forced vibrations of a, 47 



Nodal lines, of a membrane, 143, 144, 

 148 



of a plate, 153, 154 

 Nodes, in a vibrating string, 70 



in a bar, 116, 127 



in a pipe, 171 



' Normal functions,' 101, 130 

 Normal modes of vibration, 44 

 Notes, musical, 3, 285 



Ohm's law, 2, 285, 289 



Organ pipe, normal modes of, 171 



corrected theory of, 266 



mode of action of, 276 

 Overtones, 5 



influence of, on quality, 286 



on the definition of consonant 

 intervals, 288 



Pendulum, 8, 16 

 Blackburn's, 35 

 double, 38 



Period-equations, graphical solution 

 of, 83, 125, 126, 128, 256, 258 



Permanency of type, condition for, in 

 air-waves, 174 



Pipe, normal modes of a, 171 

 modulus of decay of a, 270 

 velocity of sound in a narrow, 193 



Plane waves in an elastic medium, 118 

 in air, 160, 174, 223 



Plate, transverse vibrations of a cir- 

 cular, 153 ; of a square, 154 



Plucked string, theory of, 66, 98 



Poiseuille's law, 195 



Poisson's ratio, 111 



'Quality' of musical notes, 4 

 influence of overtones on, 286 



Beciprocity, principle of, 47, 81 



