The Freedom of a String
Some stringed instruments give forth tones which are clear and sweet, but withal thin and lacking in richness and fullness. The tones sounded by two different strings may agree in pitch and loudness and yet produce quite different effects on the ear, because in one case the tone may be much more pleasing than in the other. The explanation of this is, that a string may vibrate in a number of different ways.
Touch the middle of a wire with the finger or a pencil, thus separating it into two portions and draw a violin bow across the center of either half. Only one half of the entire string is struck, but the motion of this half is imparted to the other half and throws it into similar motion, and if a tiny A-shaped piece of paper or rider is placed upon the unbowed half, it is hurled off.
If the wire is touched at a distance of one third its length and a bow is drawn across the middle of the smaller portion, the string will vibrate in three parts; we cannot always see these various motions in different parts of the string, but we know of their existence through the action of the riders.
Similarly, touching the wire one fourth of its length from an end makes it vibrate in four segments; touching it one fifth of its length makes it vibrate in five segments.
In the first case, the string vibrated as a whole string and also as two strings of half the length; hence, three tones must have been given out, one tone due to the entire string and two tones due to the segments. But we saw in Section 267 that halving the length of a string doubles the pitch of the resulting tone, and produces the octave of the original tone; hence a string vibrating as in Figure 183 gives forth three tones, one of which is the fundamental tone of the string, and two of which are the octave of the fundamental tone. Hence, the vibrating string produces two sensations, that of the fundamental note and of its octave.
When a string is plucked in the middle without being held, it vibrates simply as a whole, and gives forth but one note; this is called the fundamental. If the string is made to vibrate in two parts, it gives forth two notes, the fundamental, and a note one octave higher than the fundamental; this is called the first overtone. When the string is made to move as in Figure, three distinct motions are called forth, the motion of the entire string, the motion of the portion plucked, and the motion of the remaining unplucked portion of the string. Here, naturally, different tones arise, corresponding to the different modes of vibration. The note produced by the vibration of one third of the original string is called the second overtone.
The above experiments show that a string is able to vibrate in a number of different ways at the same time, and to emit simultaneously a number of different tones; also that the resulting complex sound consists of the fundamental and one or more overtones, and that the number of overtones present depends upon how and where the string is plucked.
FIG. - Only one half of the string is bowed, but both halves vibrate.
FIG. - The string vibrates in three portions.
FIG. - When a string vibrates as a whole, it gives out the fundamental note.