182 SOUND very small distance, a a', fig. 16, making equal excursions on one side and the other of the position of equilibrium m m' ; and as the pis- ton vibrates like a pendulum, it will increase FIG. 16. in velocity as it goes from a or from a 1 to m m', and diminish in velocity as it goes from m m 1 to a or to a'. Let T be the time taken by the piston to make a semi-vibration, that is to say, a motion from a to a' or from a' to a. Divide this time T into exceedingly small and equal parts , during which the piston will also go over very small but unequal spaces, increasing with the velocity from a to m m', and diminishing with the velocity as the pis- ton goes from m m' to a'. The first very small displacement of the piston, accomplished du- ring the time , will produce in a very thin layer of air, which touches the piston, a very feeble degree of compression, and this com- pression will progress forward into the air of the tube. The very small succeeding motion of the piston during the next succeeding t will produce a slightly greater condensation, which will travel behind the former conden- sation with the same velocity. The third dis- placement of the piston will produce a still greater condensation, and so on, until the dis- placement which brings the piston to the po- sition m m', which, being the greatest of all, will produce the greatest condensation. If the piston continues its motion to a', with a velocity which is now gradually decreasing, a new series of condensations will take place, less and less in degree, .which will travel be- hind those of the first series. These two se- ries will be symmetrically placed on one side and the other of the maximum condensation, if we suppose that the two semi-oscillations of the piston are equal, and if we neglect the very small amplitude of oscillation a a'. If a A' is the space through which the first con- densation progresses in the time T, then all the condensations which have succeeded it during the movement of the piston from a to a will be distributed in the space a' A'. If we represent by ordinates these condensations at the moment when, the piston having ar- rived at a', the first condensation is at A', we will form a curve a f a A', whose maxi- mum ordinate M a will represent the conden- sation produced by the piston at the moment of its passage through m m'. Let us now sup- pose that the vibrating piston returns on its path, it will produce by this motion a series of increasing dilatations during the time T, and then decreasing dilatations until the in- stant when the piston reaches a. These dila- tations will travel behind the condensations, and when the piston has returned to a, in which case the series of condensations will have reached the position A' a A, these dila- tations will be distributed in the space a A', and the diminution of density of the lay- ers of air can be represented by the nega- tive ordinates of the curve a (3 A', below the axis of the curve a A'. The state of air in the tube at the instant when the vibrating piston, departing from a, arrives at n p, m m', n 1 p a is indicated by the curves n N, m M, n' N', a 1 A'. If the piston makes another com- plete vibration from a to a! and from a' to , a new series of condensations and of dilata- tions, distributed in a space equal to a A, will travel behind the first series already described. The dilatation and condensation contained in a 1 A, and produced by a complete vibration of the body at the origin of sound, i. e., by an oscillating motion from a to a' and back from a' to a, is called a sonorous wave. A sonorous wave is always formed of two parts, one half of air in a state of condensation, the other half of rarefied air. The sum of all the condensations in the condensed half of the wave is represented by the area of the curve a' a A'; and if we divide this by the interval T of a half vibration of the body, we have the mean condensation of the half wave. This mean condensation can be calculated, and it has been found that for the sound given by 250 vibrations per second, which corresponds nearly with the lowest of the violin, this compression gives for the compressed half of the wave an increase of ^ to the ordinary density of the atmosphere. The length of a wave is evidently the distance through which the air has been affected the moment after the first complete vibration of the sonorous body has been made. If we designate this length by Z, we can calculate the wave length by di- viding the velocity v of sound in a second by n, the number of vibrations the sounding body makes in a second ; or, 1=^. By a sonorous wave surface is understood that surface which is at such a distance from the point or points of origin of the sound that all points in that surface have the same phase of vibration at the same instant of time. Thus, it is evident that if we have a small sphere of air which successively and rapidly increases and dimin- ishes its volume, we shall have alternate spher- ical shells of compressed and of rarefied air surrounding the vibrating sphere. If we view a surface in one of these shells, in every part of which surface the particles of air are mov- ing in the same direction with the same ve- locity, we shall have the sonorous wave sur- face. The acoustic wave lengths and wave surfaces are not mere creations of the imagi- nation, but have a real existence. The author of this article first devised a method by which one can readily detect the phases of vibration in the air surrounding a sounding body, and
