HANDBOOK OF ACOUSTICS - online book

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

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108
HAND-BOOK OF ACOUSTICS.
commencement of the 3rd. At this instant, as the student will perceive, bothwill be at (c), C, moving up, and E| down.
Now the effect of C| moving upwards is to swing the particles of air at this point upwards also, with a certain amount of force; and the effect of E| moving downwards, is to swing the same particles upwards also, with the same amount of force; Ct and E| there­fore, combine their forces to swing the air particles at (c) upwards. At the expiration of another second E| will be back again at (c) but moving now upwards, and C2 will also be at the same point moving downwards. The air particles at (c) will now be swinging down­wards, with the combined forces of E, and 02. Thus it will be seen that (c) is a point of maximum vibration, that is, the middle of a ventral segment.
The half segment in (B) fig. 56 is seen to be one-third as long as the half segment in (A); therefore the length of the sound wave emitted by (B) must be one-third the length of that emitted by (A); that is, the note corresponding to the vibrational form (B), has three times the vibration number of that corresponding to (A).
The next simplest way in which the air column in a stopped pipe can vibrate is with three nodes, as represented in (C), fig. 56 ; the next simplest, with four nodes (D), the next with five, and so on. As the length of the half segment in (0) is one-fifth the length of that in (A), the wave length of the note corresponding to the vibrational form (C), must be one-fifth of that corresponding to (A), that is, its vibrational number is five times as great. Similarly in D, it is seven times as great. Summing up, then, we find theoretically'that the vibration rates of the tones, which can be pro­duced from a stopped tube, are as the odd numbers 1, 3, 5, 7, &c, no tone intermediate in pitch between these, being possible. This can be easily verified experimentally, by the aid of an ordinary stopped organ pipe. On blowing very gently, the fundamental, which we may call (d|), is heard; on gradually increasing the force of the blast, a point is reached at which this fundamental ceases, and the (s) an octave and a fifth above, springs forth; still further increase the wind pressure, and this gives place to the (n1) two octaves and a major 3rd above the fundamental. By no variation in the blowing can any tone intermediate in pitch between these be obtained; and the vibration numbers of these three notes (d|), (s), and (m1), are as 1, 3, and 5, and thus the results obtained above are corroborated experimentally.
As before observed, sounds thus successively obtained from a pipe, by variation in the wind pressure, may be conveniently termed