ACOUSTICS 119 holtz s theory of timbre, the peculiarities depend by which any one voice may be unmistakably distinguished from every other. Voices in which overtones abound are sharp, and even rough; those in which they are few or faint, are soft and sweet. In every voice, however, the number and relative intensity of the overtones depend on the form assumed by the cavity of the mouth, which acts relatively to the vocal chords precisely as a resonator does to a tuning-fork, or a pipe to a reed. This may be easily tested by holding a tuning-fork before the open mouth, when, by giving to the cavity a suitable form, the fundamental or some overtone of the fork may be heard distinctly reverberated from the interior of the mouth. Each vowel sound, as Helinholtz has shown, is simply the result of the reinforcements by the air in the cavity of the mouth, and its prolongation towards the larynx, of one or in some cases two overtones of determinate pitch, contained in the sound which proceeds from the vocal chords. Koenig assigns the following notes as characteristic of the simpler vowel sounds (adopting the foreign pro nunciation) : To U, the note Bb below the line in the G clef, corresponding to 225 vibrations per second; to 0, the next higher octave, consequently of double the number of vibrations, and thence ascending by octaves for A, E, and I, the last of which is therefore characterised by a note of 3600 vibrations per second. The above theory of vowel sounds may be satisfactorily confirmed by means of tuning-forks, vibrating in front of resonant cavities, which can, by suitable combination, be made to utter any vowel sound. Works on Acoustics. Chladni, Traite d Acoustique. Paris, 1809. Herschel, Sir John, Encycl. Metrop., art. " Sound." Lon don, 1830. Tyndall, Lectures on Sound, 2d edit. London, 1869. Helmholtz, Die Lehre von der Tonempfindungen, 3d edit. Braunschweig, 1870, of which there is a French trans lation, and an English one is promised. Besides the above, some account of the subject is to be found in such general works on Physics as Ganot s, 14th edit., Paris, 1870, of which a translation is published by Longmans, London ; Deschanel s Natural Philosophy, translated by Prof. Everett, London, 1873; Jamin, Cours ds Physique, 3d edit., Paris, 1871; Wulner, Physik, 2d edit, Leipzig, 1870. (D. T.) Air, essential for hearing, . . 3 velocity of sound in, . 17,18,22 Amplitude of vibrations, . . 4 Beats, how produced, . . . 102 examples of, . . . 103 application to finding n for any note, . . . 104 tuning by, . . . 105 rapid effect of, on ear, . 106 Bell in vacua, .... 3 Chemical harmonicon, ... 87 Chladni s figures, . . . 69 to 71 Communication of vibrations, . 92, 93 De la Tour s syren, ... 49 Density, variations in, by longitu dinal vibrations, ... 14 Diatonic scale, . . . . 46 Difference tones, . . . . 106 Dove s syren 50 Echoes, . .... 38 Elasticity, 15 Flames, singing, .... 89, 90 Flame manometer, . . .91, 103 Fundamental note, ... 57 Gas harmonica, . . . .87, 103 Gases, velocity of sound in, . . 21, 84, 93 Harmonics in strings, . . . 57 to 60 rods, . . . 67 pipes, . . . 77 to 80 Harmony, laws of, ... 45, 46 Helmholtz, his double syren, . 51, 99 on resultant tones, . 107 on timbre, . . 108 Intensity of sound at different distances, . . 29 in air of different densities, . 30 promoted by sheet of water, &c., 39 depends on amplitude of vibra tions, ..... 41 Interference of sound laws of, . . . . .94, 95 examples of, . . . .98 to 100 Intervals, musical, ... 45 Koenig s phonautograph, . . 53 flame manometer, . . 91, 100 denial of summation-tones, 107 Kundt s experiments, ... 93 Laplace s corrected velocity of sound in air, .... 16 Lenses, acoustic, .... 34 Liquids, velocity of sound in, . 25 Longitudinal vibrations, . . S, 28 ALPHABETICAL INDEX. The minerals refer to the sections. Loudness (vid. intensity). Melde s experiments on vibrating strings, ..... 66 Membranes, vibrations of, . . 72 Musical sounds and noises, . . 44 notes, vibration-ratios of, 45 Newton s investigation of velocity in air, 15 Nodes, 54 Noises and musical sounds, . . 44 Overtones (vid. harmonics). Parabolic reflectors, ... 37 Phase, ..... 7 Phonautograph, .... 50 Pipes, Bernouilli s theory of, . 75 stopped (at both ends) . 77 open, .... 78 stopped, .... 79 harmonics in, . . . 80 open and stopped, of equal lengths, .... 81 influence of length of, on pitch, 82 length of C pipe, . . 83 defects of theory, . . 85 illustrations by manometer, 91 Pitch, depends on n, . . , 42 Plates, square, vibrations of, . 69, 70 circular, do. . . 71 interference in, . . 96, 97 Rankine s investigation of velocity of sound 15 Reeds and reed-pipes, . . . 86 to 88 Reflexion, laws of, ... 35 to 39 total, .... 33 Refraction, laws of, . . . 31 to 34 Rods, transversal vibrations of, . 67 longitudinal vibrations of, . 74 Savart s toothed wheel apparatus, 47 Scales, diatonic and chromatic, . 46 Seebeck s syren, .... 48 Solids, velocity of sound in (longi tudinal), ..... 25, 26 Solids, velocity of sound in (trans versal), . . . . 27, 28 Solids, velocityof sound in, Kundt s method, ..... 92 Stationary waves, . . 54 Strings, musical, laws of, . . 56 to 65 fundamental and overtones of, . 57, 58 overtones how obtained from, 69 Strings, musical, comparison of fun damental notes due to trans versal and -lon gitudinal vib rations, . . 60 influence on pitch of length, ten sion, &c., . 61 Melde s experi mental illus trations, . 66 Spheroidal reflectors, . . 36 Summation tones, . . 106 Syren of Seebeck, . . 48 of De la Tour, . . 49 of Dove, . 50 of Helmholtz, . . 51 Thunder, roll of, . . 40 Timbre, . . 43, 108 Tones, major, minor, and semi, . 46 Transversal vibrations, . . 9, 28 Tuning by beats, . . . . 105 Tuning-forks, mode of vibration, . 68 interference in . 97 beats in, . . 103 Ventral segments, ... 54 Vibrations, sound due to, . . 2 laws of, . . 4, 5 of pendulum, . . 4 transmission of, . 6 longitudinal and trans versal, ... 9 relation between fre quency of, and length of wave, . . 13 communication of, . 92, 93 number of, for any note determined by beats, 104 Vibrograph, .... 52 Voice, its seat in vocal chords, . 109 Vowel sounds, how accounted for, 109 Water, velocity of sound in, . 30 Waves of displacement, . . 10,12 of Telocity, . . . 11, 12 of condensation and rare faction, ... 14 lengths of, ... 10 relation of, to n, 13 propagation of, . . . 13
Weber s theory of reed-pipes, , 88
