Wave Motion and Interference
5
wave of longitudinal vibrations passes along it, announcing its arrival at the other end by a sound at the box; the time occupied in the passage being perceptibly less than that required for the transverse wave.1
The velocity of the wave is in both cases too great to admit of convenient investigation. In order to familiarize the student with wave motion, a number of mechanical devices have been constructed, such as that shown in Fig. 1. Such me- FIG- 2
chanical models imitate wave motions rather than produce them. They are purely kinematic illustrations, and not true wave motions; for in the latter the propagation is determined by the forces and inertias which exist within the system of particles through which the wave is moving.
The wave model of Lord Kelvin is free from this objection. It consists of a vertical steel wire on which blocks of wood are fastened at regular intervals. It is very essential that these blocks should not slip on the wire, and this end is best accomplished by bending the wire, in the middle of each block, around three small nails, as shown in Fig. 2. For the sake of symmetry two such pieces may be fastened together, with the wire passing between them. Attention may be fixed upon the motion of the ends of the blocks, by driving into them large, gilt, upholstering tacks—a device which adds considerably to the attractiveness of the experiment. The complete apparatus is shown in Fig. 3.
On giving the lowest element a twist, the torsion produced in the wire will communicate the twist to the next element, etc. The twist thus travels along the entire row,
i1 am indebted to Professor Cross for this illustration.
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6
Light Waves and Their Uses
moving more slowly the smaller the wire and the heavier the blocks, so that, by varying these two factors, any desired speed may be obtained.
The wave form which is propagated in any of the various possible cases is, in general, very complicated. It can be shown, however, that it is always possible to express such forms, however complex, by a series of simple sine curves such as that represented in Fig. 4. The study of wave motion may be much simplified by this device. Accordingly, in all that follows, except where the contrary is expressly stated, it will be assumed that we are dealing with waves of this simple type.
There are certain characteristics of wave motion of which we shall have to speak frequently in what follows, and which therefore need definition. In the first place, the shape of the wave illustrated in Fig. 4 is important. It is the curve which would be drawn by a pendulum, carrying a marker, upon a piece of smoked glass moving uniformly^at right angles to the motion of the pendulum. Since the pendulum moves in what is called simple harmonic motion, the curve is called a simple harmonic curve, or a sine curve. The amplitude of the wave is the maximum distance of a crest or a trough from the position of rest, i. e., from the straight line drawn through the middle of the curve. The period of the vibration is the time it takes one particle to execute one complete vibration; i. e., to revert to the pendulum, it is the time it takes the pendulum to execute