CHAPTER III.

ON RESONANCE.

37. WHEN a sounding body causes another body to emit sound, we have an instance of a a very remarkable phenomenon called resonance. The German term for it, 'co-vibration' (Mitschwingung), possesses the merit of at once indicating its essential meaning, namely the setting up of vibrations in an instrument, not by a blow or other immediate action upon it, but indirectly as the result of the vibrations of another instrument. In order to produce the effect, we have only to press down very gently one of the keys of a pianoforte, so as to raise the damper without making any sound, and then sing the corresponding note loudly into the instrument. When the voice ceases, the instrument will continue to sustain the note, which will then gradually fade away. If the key is allowed to rise again before the sound is extinct, it will abruptly cease. A similar experiment may be tried, as follows, on any pianoforte which allows the wires to be uncovered. Each note is, as is well known, produced by two or by three wires. Having, as in

the previous case, raised one of the dampers without striking the note, twitch one of the corresponding wires sharply with the finger-nail, and then wait a few seconds. The vibrations will, during this interval, have communicated themselves to the other string or strings belonging to the note pressed down: if, therefore, the first wire be now stopped by applying the tip of the finger to the point where it was at first twitched, the note heard will continue to be sustained by the remaining wire or wires.

A more instructive method of studying resonance is to take two unison tuning-forks, strike one of them, and hold it a short distance from the other. The second fork will then commence sounding by resonance, and will continue to produce its note if the first fork be brought to silence. It is essential to the success of this experiment that the two forks should be rigorously in unison. If the pitch of one of them be lowered by causing a small pellet of wax to adhere to the end of one of its prongs, the effect of resonance will no longer be produced, even though the alteration of pitch be too small to be recognised by the ear. Further, the phenomenon generally requires a certain length of time to develope itself; for, if the silent fork be only momentarily exposed to the influence of its sounding fellow, hardly any vibration is communicated. The reso

nance is at first extremely feeble, and gradually increases in intensity under the continued action of the originally-excited fork. Some seconds must elapse before the maximum resonance is attained. The conditions of our experiment show that the resonance of the second fork was due to the transmission by the air of the vibrations of the first, the successive air-impulses falling in such a manner on the fork as to produce a cumulative effect. If we bear in mind the disproportionate mass of the body set in motion compared to that of the air acting upon it,-steel being more than six thousand times as heavy as atmospheric air for equal bulks-we cannot fail to regard this as a very surprising fact.

Let us examine the mechanical causes to which it is due. Suppose a heavy weight to be suspended from a fixed support by a flexible string, so as to form a pendulum of the simplest kind. In order to cause it to perform oscillations of considerable extent by the application of a number of small impulses, we proceed as follows. As soon as, by the first impulse, the weight has been set vibrating through a small distance, we take care that every succeeding impulse is impressed in the direction in which the weight is moving at the time. Each impulse thus applied will cause the pendulum to oscillate through a larger angle [§ 19] than before, and, the effects of many

impulses being in this way added together, an extensive swing of the pendulum is the result.

When the distance through which the weight travels to and fro, though in itself considerable, is small compared to the length of the supporting string, the time of oscillation is the same for any extent of swing within this limit, and depends only on the length of the string. My readers will find this important principle illustrated in any manual of Elementary Mechanics, and I must ask them to take it for granted here. For the sake of simplicity, let us suppose that we are dealing with a pendulum of such a length as to perform one complete oscillation in each second, and therefore to make a single forward or backward swing in each half second. It will be clear, from what has been said above, that the maximum effect will be produced on the motion of the pendulum by applying a forward and a backward impulse respectively during each alternate half-second, or which is the same thing, by administering a pair of to-and-fro impulses during each complete oscillation of the pendulum. We have a simple instance of such a proceeding in the way in which two boys set a heavily-laden swing in extensive motion. They stand facing each other, and each boy, when the swing is moving away from him, helps it along with a vigorous push.

38. The above considerations enable us to explain how a sounding fork can set another fork in unison with itself into vibration by the action of the intervening air. When a continuous musical note is being transmitted, we know that, at any one point we choose to fix upon, the air is undergoing a series of rapid changes, becoming alternately denser and less dense than it would be but for the passage of the sound. The increase of density is accompanied by an increase of pressure; its diminution by a diminution of pressure [§ 20].

Fig. 21.

dac

B

Let A, Fig. 21, be the sounding fork, B that whose vibrations are to be excited by resonance, and let us consider the effect of the alternations of pressure of the air at a on the prong ba. Let the first pulse which arrives at a be one of condensation, and let its increased pressure cause the prong ba to swing as far as be1. The elastic recoil of the fork would alone cause the prong to spring back to an equally inclined position on the other side of ba. Since,

The extents of vibration shown in this figure are of necessity enormously exaggerated.