Page:The American Cyclopædia (1879) Volume I.djvu/91

 ACOUSTICS n ments, are produced. In the trombone, the length of the tube is increased and diminished by a sliding arrangement ; while in the cornet u piston and similar brass instruments, the same elongation and shortening is produced by piston valves admitting or shutting off the air from side channels of greater or lesser length. In stringed instruments the same results are accomplished by different length of strings. As in the organ every pipe produces only a single tone, so in the pianoforte every string is intended for one tone; while in the harp, by a slight shortening, the pitch of each string may be raised a so-called semitone. In all the other stringed instruments, as the violin, violoncello, and guitar, the different tones are produced by the use of very few strings only, which, however, by proper manipulation with the fingers, may be shortened so as to produce tones of which the vibrations become faster in proportion as the sounding portion of the string is shortened. In regard to the law governing their vibration, it is the same for strings as for pipes. Other circumstances being equal, their velocity is inversely proportional to the length of the pipe or string. The tone of strings also changes by change of tension, and the velocity of their vibration is in the ratio of the square root of the weights which pro- duce this tension. Further, the tone depends upon the thickness of the string, its rigidity, weight, and nature of material. When a string is subdivided into a number of equal parts, these parts will vibrate simultaneously, leaving the points of division at rest, and produce the harmonic tones, after the same law as in the case of a column of air in the French horn. The subjoined five figures give the manner of vibration of a string as a whole, half, third, fourth, and fifth parts, producing different FUNDAMENTAL TONE. DOUBLE OCTAVE. THIRD. Harmonic Sound Waves of a String. tones, the harmonics of the fundamental tone, its octave, fifth above or twelfth, its double octave, and third above that, or seventeenth. On the violin these subdivisions may be effect- ed by slightly touching the string on one of the points dividing it into equal parts, and the harmonic upper tones thus produced are called the flageolet tones. In the ^Eolian harp, in which the strings are put into vibration by the friction of a current of air, these divisions are incidentally and continually changing, and thus a variety of harmonic tones is produced. The division points, where the string happens to be at rest, are called nodal points. An elastic plate of glass, brass, steel, or other suitable material, may also be made to vibrate and emit tones ; and when fixed at one point and excited at one of its edges by a violin bow, it may be made to produce a considerable variety of tones,. by the fact that it may be subdivided into various systems of nodal lines ; the spaces between these lines are the sounding portions, and the vibrations are more rapid or the tones sharper in proportion as these spaces are small- er. These nodal lines may be made visible by scattering dry sand over the plate, and when it is put into vibration with the violin bow, the grains of the sand which are not on the nodal lines will be thrown aside, and not come to rest until they are accumulated upon the nodal lines. Thus many kinds of regular and almost geometrical figures may be formed, which are called, after the inventor of this method, Chladni's nodal sound figures. With different forms of plates, many hundreds of such figures have been obtained. Our figures illus- trate only a few of the most remarkable. The first and most simple is produced by the lowest Chladnfs Nodal Sound Figures. tone which can be obtained from the disk ; the others belong to higher and higher tones, while the last and most complicated is produced by the highest tone ; in this case the smallest parts of the glass disk vibrate for themselves, and produce then the most rapid vibrations. It is thus seen that every tone which may be