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new condensation, LM, to be formed further on, and itself becoming the rarefaction KL, co-operating, at the same time, with the advancing piston to produce in its own rear the condensation HK. In (5) the piston is again where it was in (3). HK has expanded into the rarefaction NO, KL contracted into the condensation OP, LM expanded into the rarefaction PQ, and a new condensation, QR, been formed in front.

The figure makes it clear that each forward stroke of the piston produces a pulse of condensation, and each backward stroke a pulse of rarefaction; but that, when once formed, these pulses travel onwards independently of any external force. They do so, as we have seen, in virtue of the relation which connects the pressure of the air with its density, in other words, on the elasticity of the air.

If we suppose our moveable piston withdrawn from the tube, and a vibrating tuning-fork held with the extremity of one prong close to the orifice of the tube, the conditions of the problem will not be essentially modified. Each outward swing of the will give rise to a condensed, and each inward swing to a rarefied pulse, and thus, during every complete vibration of the fork, one sonorous wave, consisting of a pulse of condensation and a pulse of rarefaction, will be started on its journey along the tube.


22. We have examined the transmission of Sound along a column of air contained in a tube of uniform bore. A more important case is that in which a sound, originated at an assigned point, spreads out from it freely in all directions. Here we must conceive a series of spherical shells, alternately of condensed and of rarefied air, one inside the other, and all having the point of origination of the sound as their common centre. All the shells must be supposed to expand uniformly like an elastic globular balloon constantly inflated with more and more gas. The great difference between this case and that last considered lies in this, that, as the spherical shells of condensation and rarefaction spread, it is necessary, in order to keep up the wave-motion, to throw larger and larger surfaces of air into vibration; whereas within the tube the transverse section remained the same throughout. Hence, as the same amount of original disturbing force has to set a constantly increasing number of air-particles into motion, it can only do so by proportionately shortening the distances through which the individual particles move, i. e. by diminishing their extent of vibration. Accordingly when Sound-waves spread out freely in all directions, the further any given air-particle is from the point at which the sound originated, the smaller will be the extent of the

vibration into which it will be thrown when the waves reach it.

23. Sounds are either musical or non-musical. The vast majority of those ordinarily heard-the roaring of the wind, the din of traffic in a crowded thoroughfare-belong to the second class. Musical sounds are, for the most part, to be heard only from instruments constructed to produce them. The difference between the sensations caused in our ears by these two classes of sounds is extremely well marked, and its nature admits of easy analysis. Let a note be struck and held down on the harmonium, or on any instrument capable of producing a sustained tone. However attentively we may listen, we perceive no change or variation in the sound we hear. A perfectly continuous and uniform sensation is experienced as long as the note is held down. If, instead of the harmonium, we employ the pianoforte, where the sound is loudest directly after the moment of percussion, and then gradually dies away, the result of the experiment is that the diminution of loudness is the only change which occurs: the effect produced is the same as if our harmonium had, while sounding out its note, been carried gradually further and further away from us.

In the case of non-musical sounds, variations of a different kind can be easily detected. In the howl

ing of the wind the sound rises to a considerable degree of shrillness, then falls, then rises again, and so on. On parts of the coast, where a shingly beach of considerable extent slopes down to the sea, a sound is heard in stormy weather which varies from the deep thundering roar of the great breakers, to the shrill tearing scream of the shingle dragged along by the retreating surf. Similar variations may be noticed in sounds of small intensity, such as the rustling of leaves, the chirping of insects, and the like. The difference, then, between musical and nonmusical sounds seems to lie in this, that the former are constant, while the latter are continually varying. The human voice can produce sounds of both classes. In singing a sustained note it remains quite steady, neither rising nor falling. Its conversational tone, on the other hand, is perpetually varying in height even within a single syllable; directly it ceases so to vary, its non-musical character disappears, and it becomes what is commonly called 'sing-song.'

We may then define a musical sound as a steady sound, a non-musical sound as an unsteady sound. It is true we may often be puzzled to say whether a particular sound is musical or not: this arises, however, from no defect in our definition, but from the fact that such sounds consist of two elements, a musical and a non-musical, of which the latter may

be the more powerful, and therefore absorb our attention, until it is specially directed to the former. For instance, a beginner on the violin often produces a sound in which the irregular scratching of the bow predominates over the regular tone of the string. In bad flute playing, an unsteady hissing sound accompanies the naturally sweet tone of the instrument, and may easily surpass it in intensity. In the tones of the more imperfect musical instruments, such as drums and cymbals, the non-musical element is very prominent, while in such sounds as the hammering of metals, or the roar of a water-fall, we may be able to recognize only a trace of the musical element, all but extinguished by its boisterous companion.

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We have seen that Sound reaches our ears by means of rapid vibrations of the particles of the atmosphere. It has also been shown that steadiness is the characteristic feature of musical, as distinguished from non-musical, sounds. We may infer hence that the motion of the air corresponding to a single musical sound will be itself steady, i.e. that equal numbers of equal vibrations will be executed in precisely equal times. This conception of the physical conditions under which musical sounds are produced will suffice for the present. We proceed to consider in detail the various ways in which such

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