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V. § 57.] SOUNDS OF ORGAN PIPES. 117
which a wire presents to the air is so small that, but for the aid of the sound-board, its vibrations would hardly excite an audible sound. The reader will not fail to notice that the sound-board of the pianoforte plays the same part as the hollow cavity of the violin, and is in fact a solid resonator. In the harp, the framework of the instrument serves the same purpose. We have, in this combination of a vibration-exciting apparatus with a resonator, the type of construction adopted in nearly all musical instruments.
3. Sounds of organ-pipes.
57. It has been shown [§ 51] that, when two series of equal waves due to transverse vibrations travel along a stretched wire in opposite directions, stationary nodes are formed at equal distances along it, separated by vibrating segments of equal lengths. Let us now suppose that two series of equal waves due to longitudinal vibrations are traversing, in opposite directions, a column of air contained in a tube of uniform bore. Each set of such waves has its own associated wave-form [§ 18, p. 37]. We have only, therefore, to consider the curves drawn in Fig. 35 as associated waves corresponding to longitudinal air-vibrations, in order to make the conclusions of § 52 at once applicable to the case in hand. The result is a series of equidistant nodes, or points of per-