A Dictionary of Music and Musicians/Node

by James Lecky

NODE (Latin nodus, a knot). The vibration of a string may assume many different forms. In Fig. 1 the string is shewn vibrating as a whole; in Fig. 2 it divides into two equal segments; in Fig. 3 into three equal segments. These segments, where the amplitude of vibration is greatest, are called Loops (l, Figs. 2 and 3), and the points of rest between them are called Nodes (n).

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.

But when a string is plucked, as in the harp and guitar, or bowed as in the violin, it does not vibrate in any one of the simple forms just described, but in several of them at once. The motion of the whole string combined with that of its halves would be represented by Fig. 4. Here the node is no longer a point of complete rest but a point where the amplitude of vibration is least.

If the string while vibrating be touched at ½, ⅓, ¼, etc. of its length, as in playing harmonics on the harp or violin, all forms of vibration which have loops at these points vanish, and all forms which have nodes there become more marked. Thus it is possible to damp the vibrations of the whole string, of its third parts, of its fifth parts, etc., leaving the vibrations of its halves, of its fourth parts, of its sixth parts, etc., unimpeded.

The column of air in an open pipe vibrating as a whole has a node in the centre, towards which the particles of air press and from which they again draw back (see Fig. 5, n).

Fig. 5.

Thus at the node the air does not move but undergoes the greatest changes of density. At the loop (l) there is no change of density but great amplitude of vibration. The open ends of the pipe are always loops, for the density at these points being the same as that of the outer air, does not change. This remains true whether the pipe have two, three, or more nodes, as shewn in Figs. 6 and 7.

Fig. 6.
Fig. 7.

In a stopped pipe the closed end is always a node, and the open end a loop, whether the column of air vibrate as a whole (see Fig. 8), or divide into segments as shown in Figs 9 and 10.

Fig. 8.
Fig. 9.
Fig. 10.

In practice both an open and a stopped pipe vibrate not in any one of the ways just described, but in several of them at once. Here, too, as in the case of strings, the node is not a point of complete rest but of least motion.

Chladni showed that sand strewn on vibrating plates or membranes collects along the lines where the motion is least. These are called nodal lines, and may assume a variety of symmetric forms.

[ J. L. ]