NODAL POINTS AND LINES. Nodal points are those points in the length of a string extended between two fixed objects, or in a column of air confined at one or at each extremity, which, when the string or column is put in a state of vibration, are found to remain at rest ; nodal lines are corresponding lines which exist on the surface of an elastic body, usually a plate, whose parts arc in a state of vibration.
It Is well known that if -a string or a metallic cord be attached at its extremities to a board or plate, on causing it, when in a state of tension, to vibrate transversely, there may be distinguished, besides the principal sound, which is due to the length of the string, several others which have a greater degree of acuteness; these are called harmonic sounds, and they are conceived to result from some property of the extended string, by which, when in a state of vibration, it becomes a sort of moving axis, having on it points, at distances from one another equal to some aliquot part of the whole length of the string, at which points a contrariety in the directions of the vibrations of the particles keeps the latter in a state of rest. Such are called nodal points ; snd they may be conceived to form themselves in con sequence of inequalities in the thickness or density of the string, or of different degrees of flexibility in its different parts. The string between every two such points is in the same condition as if it were attached at there points to fixed objects ; its partial vibrations are consequently such as are due to the distances between the points, and hence arise the secondary or harmonic sounds.
A string of considerable length, on being made to vibrate, will be found to Lave several such nodal points, and the curves which the intervals assume in consequence of the vibrations, though alternately on opposite sides of the axis of the string, are equal and similar to one another. The situations of the nodal points may be made evident by placing, at intervals, across the string, pieces of paper notched or bent in the form of an inverted V ; those which are at the places of the nodes remaining at rest, while the others experience considerable agita tions, or are thrown entirely off.
If a string, in a state of tension, have its extremities attached to a board or plate of metal, and be made in some part of its length, to pass over a bridge resting in the centre of the board or plate, the vibrations of the string, when a violin-bow is drawn across it, will be communi cated to the plate ; and if over the latter some light dust or powder such as fine sand or lycopodium be sifted, that dust will be agitated and made to arrange itself on lines at which the surface of the plate is in a state of rest : these are called nodal lines, and the figures which they form are called Acoustic figures. Again, if a glass rod be cemented at
one end to the centre of a disk of the like material, and be excited by being rubbed, for example, with a wet cloth, so as to be put in a state of vibration longitudinally, those vibrations will be communicated to the disk, and light dust strewed over the latter when in a horizontal position will arrange itself in acoustic figures. Or, if a glass rod be connected at each extremity to a glass disk at right angles to its length, on exciting one of the disks by drawing a violin-bow across its edge, the vibrations of that disk will, by means of the rod, be communicated to the other ; and if light dust be strewed over both it will arrange itself in figures : when the disks are equal and similar to one another, the figures are alike on both ; otherwise they differ.
If a column of air in a cylindrical tube which is closed at either or at each end be acted upon by the force of the breath, for example, applied at an aperture in any part of its length ; it will spontaneously divide itself into portions in which the particles are subject to equal and similar vibrations [ACOUSTICS; VIBRATION] : these portions are separated from one another by sectional areas in which the particles are at rest; the condensations, or rarefactions, of the air being, in those areas, greater than in any other parts of the tube in consequence of the particles moving in contrary directions, and with equal velocities towards, or from, them. Such areas are called nodal sections, and several may exist at the same time in the tube. Their existence is rendered evident by boring small holes in different parts of the sides of the tube and covering them with pieces of thin paper slightly adherent to the surface : at the nodal sections the papers will be scarcely affeeted, while, in the intervals, they will be greatly agitated.