Imágenes de páginas
PDF
EPUB

undulating line is obtained on the paper, which represents fairly well the vibratory movement of the tuning-fork. When the tuning-fork gives a loud sound, the vibrations

[graphic][subsumed][subsumed][merged small]

traced on the paper are very wide; later on, when the sound is already weakened, the vibrations begin to diminish in width; finally, when the sound is on the point of ceasing, they become almost invisible, and are sensibly confounded with the straight line.

5. The vibration of a string can also be very easily demonstrated. For this purpose a metal string is used, stretched over a wooden box (fig. 4). Two bridges, A and

B, on which the string rests, give it the exact length of one metre, and a scale placed beneath it enables the length of any part to be determined at will. The wire is fixed

1

A

B

[ocr errors]

Fig. 4.

and kept stretched by means of pegs, exactly as in a pianoforte. This instrument, which has been known since the days of the ancient Greeks, and which is called a sonometer or monochord, is of great importance both in the history of music and in the study of those phenomena in which we are now interested. If the string be rubbed in the middle with a violin bow, a note is obtained, the pitch of which depends on many circumstances, as, for instance, on the length, thickness, and density of the string, and on its tension. If the string be rubbed lightly, the sound is feeble; if, on the contrary, it be rubbed with some force, the sound is loud; and, generally speaking, the intensity or loudness of the sound depends on the greater or less amount of force that produces it. The vibration of this string can be demonstrated in the following manner :

Simple observation has already shown that the string

At the

when rubbed is in a state of rapid vibration. extremities, where it rests on the two bridges, the string appears to be at rest, but when the middle part is examined, it is found that the string loses its sharpness of outline. It appears sensibly thickened, and this thickening reaches its maximum at about the middle of the string, which proves that each particle of the string performs a to-and-fro movement in a direction perpendicular to the length of the string. Vibrations of this sort are called transverse, to distinguish them from longitudinal vibrations, in which each particle vibrates in the direction of the string itself.

In practical music no use is made of the longitudinal vibration of strings; the transverse vibrations only need here be treated of. In order better to demonstrate their existence, some little slips of paper, doubled in the middle like riders, may be placed on the string; when it vibrates, these riders are thrown up on account of their lightness and fall back again on the string, thus indicating when it is in a state of vibration and when it is at rest. The most simple form of vibration is that in which the whole string performs simultaneously one single vibration. This effect can easily be obtained by leaving the string quite free, and rubbing it with the bow close to one of its ends. In that case all the riders are thrown up-first those in the middle, where the movement is greatest, and afterwards the others in succession. This shows that, with the exception of the two fixed points of the string, there is no

point of it that does not vibrate, or, in other terms, that the whole string vibrates in one single vibration. The note which is thus obtained from the string is the lowest note corresponding to it, and it is for this reason that it is called its fundamental note.

The

But this is not the only note which can be obtained from the string. If it be touched at its middle with the finger, or, better still, with a feather (fig. 4), a note is obtained which is observably higher-a note which the musical ear easily distinguishes, and which practical musicians call the octave of the fundamental note. string in this case vibrates in two parts in such a way that the point touched remains at rest. This fixed point is called a node of the vibrating string, and such a node has been produced artificially by touching the string at the point indicated. In fact, if the riders be now placed on the string, it will be observed in this case that the rider nearest to the finger does not move, whilst all the others are thrown off. The rider by remaining at rest thus indicates the presence of the node. Successively higher and higher notes can be obtained from the string by touching it at a third, a fourth, and a fifth of its length, &c. An experiment made by means of riders shows that in each case of this sort the string subdivides itself into a certain number of parts, invariably equal-in the first case into three, in the second into four, and in the third into five, &c.- and the riders that remain on the string will indicate the equidistant nodes formed

in the string. Thus, for example, if the string be touched at one-fifth of its length, it divides itself into five equal parts, and four nodes are formed at distances of,,, of the string's length, whilst at the intermediate points is

4

A

Fig. 5.

found the maximum vibratory movement (fig. 5). The parts of the string between the nodes which contain these points of maximum movement are called ventral segments.

Fig. 6.

Fig. 6 represents in somewhat exaggerated dimensions the different modes of vibration which a string assumes in different cases, when it vibrates as a whole, or is divided

« AnteriorContinuar »