Waves and ripples in water, air, and æther

by Sir J. A. Fleming

Fig. 54.

In the case of a violin or piano string, we have an example of the same action. In playing the violin, the effective length of the string is altered by placing the finger upon it at a certain point, and then setting the string in vibration by passing along it a bow of horsehair covered with rosin. The string is set in vibration as a whole, and also in sections, and it therefore yields the so-called fundamental tone, accompanied by the harmonics or overtones. Every violinist knows how much the tone is affected by the point at which the bow is placed across the string, and the reason is that the point where the bow touches the string must always be a ventral point, or anti-node, and it therefore determines the harmonics which shall occur.

Another good illustration of the action of properly intermittent small impulses in creating vibrations may be found in the following experiment with two electrically controlled tuning-forks: A large tuning-fork, F ([see Fig. 54]), has fixed between its prongs an electro-magnet, E, or piece of iron surrounded with silk-covered wire. When an electric current from a battery, B, traverses the wire it causes the iron to be magnetized, and it then attracts the prongs and pulls them together. The circuit of the battery is completed through a little springy piece of metal attached to one of the prongs which makes contact with a fixed screw. The arrangement is such that when the prongs fly apart the circuit is completed and the current flows, and then the current magnetizes the iron, and this in turn pulls the prongs together, and breaks the circuit. The fork, therefore, maintains itself in vibration when once it has been started. It is called an electrically driven tuning-fork. Here are two such forks, in every way identical. One of the forks is self-driven, but the current through its own electro-magnet is made to pass also through the electro-magnet of the other fork, which is, therefore, not self-driven, but controlled by the first. If, then, the first fork is started, the electro-magnet of the second fork is traversed by intermittent electric currents having the same frequency as the first fork, and the electro-magnet of the second fork administers, therefore, small pulls to the prongs of the second fork, these pulls corresponding to the periodic time of the first fork. If, as at present, the forks are identical, and I start the first one, or the driving fork, in action it will, in a few seconds, cause the second fork to begin to sound. Let me, however, affix a small piece of wax to the second fork. I have now altered its proper period of vibration by slightly weighting the prongs. You now see that the first fork is unable to set the second fork in action. The electro-magnet is operating as before, but its impulses do not come at the right time, and hence the second fork does not begin to move.

If we weight the two forks equally with wax, we can again tune them in sympathy, and then once again they will control each other.

Fig. 55.—An experiment on resonance.

All these cases, in which one set of small impulses at proper intervals of time create a large vibration in the body on which they act, are said to be instances of resonance. A more perfect illustration of acoustic resonance may be brought before you now. Before me, on the table, is a tall glass cylindrical jar, and I have in my hand a tuning-fork, the prongs of which make 256 vibrations per second when struck ([see Fig. 55]). If the fork is started in action, you at a distance will hear but little sound. The prongs of the fork move through the air, but they do not set it in very great oscillatory movement. Let us calculate, however, the wave-length of the waves given out by the fork. From the fundamental formula, wave-velocity = wave-length × frequency; and knowing that the velocity of sound at the present temperature of the air is about 1126 feet per second, we see at once that the length of the air wave produced by this fork must be nearly 4·4 feet, because 4·4 × 256 = 1126·4. Hence the quarter wave-length is nearly 1·1 foot, or, say, 1 foot 1 inch.

I hold the fork over this tall jar, and pour water into the jar until the space between the water-surface and the top of the jar is a little over 1 foot, and at that moment the sound of the fork becomes much louder. The column of air in the jar is 1·1 foot in length and this resounds to the fork. You will have no difficulty in seeing the reason for this in the light of previous explanations. The air column has a certain natural rate of vibration, which is such that its fundamental note has a wave-length four times the length of the column of air. In the case of the rope fixed at one end and jerked up and down at the other so as to make stationary vibrations, the length of the rope is one quarter of the wave-length of its stationary wave. This is easily seen if we remember that the fixed end must be a node, and the end moved up and down must be an anti-node, or ventral segment, and the distance between a node and an anti-node is one quarter of a wave-length. Accordingly the vibrating column of air in the jar also has a fundamental mode of vibration, such that the length of the column is one quarter of a wave-length. Hence the vibrating prongs of the 256-period tuning-fork, when held over the 1·1 foot long column of air, are able to set the air in great vibratory movement, for the impulses from the prongs come at exactly the right time. Accordingly, the loud sound you hear when the fork is held over the jar proceeds, not so much from the fork as from the column of air in the jar. The prongs of the fork give little blows to the column of air, and these being at intervals equal to the natural time-period of vibration of the air in the jar, the latter is soon set in violent vibration.

We can, in the next place, pass on now to discuss some matters connected with the theory of music. When regular air-vibrations or wave-trains fall upon the ear they produce the sensation of a musical tone, provided that their frequency lies between about 40 per second and about 4000. The lowest note in an organ usually is one having 32 vibrations per second, and the highest note in the orchestra is that of a piccolo flute, giving 4752 vibrations per second. We can appreciate as sound vibrations lying between 16 and 32,000, but the greater portion of these high frequencies have no musical character, and would be described as whistles or squeaks.