HANDBOOK OF ACOUSTICS - online book

A complete view of Acoustical Science & its bearings on music, for musicians & music students.

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18                       HAND-BOOK OF ACOUSTICS.
Let A, fig. 14 (1), represent a tuning-fork, and BC a long tube open at both ends. Suppose now, that the fork begins vibrating, its prongs first performing an outward journey. The air in BO will be condensed, but in consequence of the swiftness of the fork's motion, and the great elasticity of air, this condensation will be confined during the outward journey of the prongs, to a compara­tively small portion of the tube BC: say to the portion (ab) fig. 14 (2). The air in (ab), being now denser than that in advance of it, will expand, acting on the air in (50) as the tuning-fork acted upon it, thus causing a condensation in (be) fig. 14 (3), while the air in (ab) itself, overshooting the mark, as it were, becomes rarefied, an effect which is increased by the simultaneous retreat of the prong A. Again, the air in (be) fig. 14 (3), being denser than that before and behind, expands both ways, forming condensations (cd) and (ab) fig. 14 (4), in both directions; while in its place is formed the rarefaction (be), the formation of the con­densation (ab) being assisted by the outward journey of A. Next the air in (ab) and (cd) fig. 14 (4), being denser than that on either side, expands in both directions, forming the condensations (be) and (de) fig. 14 (5); rarefactions being formed in (ab) and (cd), the former assisted by the retreat of the prong A. By further repetitions of this process the sound waves (ac) and (ce) will be propagated along the tube.
For the sake of simplicity, the motion has been supposed to take place in a tube. This restriction may now be removed. The movement of the air passing outward in every direction from the sounding body, the successive condensations and rarefactions form spherical concentric shells round it.
In fig. 14 (5), (ac) and (ce) form two complete sound waves, (be) and (de) being the condensed, and (ab) and (cd) the rarefied parts. In studying the motion of the particles of air forming these sound waves, it will be simplest to consider those adjoining the prong A, for their motion will necessarily be similar to that of the prong itself. The first point to notice is, that the direction of particle vibration in this case is the same as that of the wave motion, and not transversely to it as in the case of the sand tube. In the next place, it will be observed, that the tuning-fork makes one complete vibration while the wave passes through a space equal to its own length; that is, each particle executes one complete vibration in exactly the same time as the wave takes to pass through a distance equal to its own length. Again, the amplitude of the wave is