Vibration of Strings—How employed in Music—Influence of Sound-Boards—Laws of Vibrating Strings—Combination of Direct and Reflected Pulses—Stationary and Progressive Waves—Nodes and Ventral Segments—Application of Results to the Vibrations of Musical Strings—Experiments of Melde—Strings set in Vibration by Tuning-Forks—Laws of Vibration thus demonstrated—Harmonic Tones of Strings—Definitions of Timbre or Quality, or Overtones and Clang—Abolition of Special Harmonics—Conditions which affect the Intensity of the Harmonic Tones—Optical Examination of the Vibrations of a Piano-Wire.
§ 1. Vibrations of Strings: Use of Sound-Boards
WE HAVE to begin our studies to-day with the vibrations of strings or wires; to learn how bodies of this form are rendered available as sources of musical sounds, and to investigate the laws of their vibrations.
To enable a musical string to vibrate transversely, or at right angles to its length, it must be stretched between two rigid points. Before you, Fig. 31 (next page), is an instrument employed to stretch strings, and to render their vibrations audible. From the pin p, to which one end of it is firmly attached, a string passes across the two bridges B and B′, being afterward carried over the wheel H, which moves with great freedom. The string is finally stretched by a weight W, of 28 lbs., attached to its extremity. The bridges B and B′, which constitute the real ends of the string, are fastened on to the long wooden box M N. The whole instrument is called a monochord, or sonometer.
Fig. 31.
Taking hold of the stretched string B B′ at its middle and plucking it aside, it springs back to its first position, passes it, returns, and thus vibrates for a time to and fro across its position of equilibrium. You hear a sound, but the sonorous waves which at present strike your ears do not proceed immediately from the string. The amount of wave-motion generated by so thin a body is too small to be sensible at any distance. But the string is drawn tightly over the two bridges B B′; and when it vibrates, its tremors are communicated through these bridges to the entire mass of the box M N, and to the air within the box, which thus become the real sounding bodies.
That the vibrations of the string alone are not sufficient to produce the sound may be thus experimentally demonstrated: A B, Fig. 32 (next page), is a piece of wood placed across an iron bracket C. From each end of the piece of wood depends a rope ending in a loop, while stretching across from loop to loop is an iron bar m n. From the middle of the iron bar hangs a steel wire s s′, stretched by a weight W, of 28 lbs. By this
Fig. 32. arrangement the wire is detached from all large surfaces to which it could impart its vibrations. Plucking the wire s s′, it vibrates vigorously, but even those nearest to it do not hear any sound. The agitation imparted to the air is too inconsiderable to affect the auditory nerve at any distance. A second wire t t′, [Fig. 33] (next page), of the same length, thickness, and material as s s′, has one of its ends attached to the wooden tray A B. This wire also carries a weight W, of 28 lbs. Finally, passing over the bridges B B′ of the sonometer, [Fig. 31], is our third wire, in every respect like the two former, and, like them, stretched by a weight W, of 28 lbs. When the wire t t′, Fig. 33, is caused to vibrate, you hear its sound distinctly. Though one end only of the wire is connected with the tray A B, the vibrations transmitted to it are sufficient to convert the tray into a sounding body. Finally, when the wire of the sonometer M N, [Fig. 31], is plucked, the sound is loud and full, because the instrument is specially constructed to take up the vibrations of the wire.