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very gently into it. The fundamental tone of the pipe which we will call (d|) will be produced. On gradually increasing the strength of the wind, a point will be reached, at which this note will vanish, and a note (d), an octave higher, will be heard. On blowing harder still, this (d) will cease, and a note (s) a fifth above will be given forth, and so on. All these notes above the fundamental, which thus apparently make their appear­ance successively, are usually termed the harmonics of the pipe.
In order to understand how these tones are produced, let us turn back to page 60. We saw there how a condensation entering one end (a) of the tube (fig. 53), proceeds to the other end and is there reflected as a rarefaction. Now suppose that at the moment this rarefaction starts back towards (a) another rarefaction starts from (a); what will happen when they meet in the centre ? The wave from (b), if none other were present, would cause the particles of air in the centre (c) to move upwards; that from (a) would move them with equal force downwards. Under these circumstances the particles in the centre will remain at rest. But, just as in the case of the string, the two pulses of rarefaction will not interfere with one another; each will pursue its course to the end of the tube, where each will be reflected, as formerly explained, as a condensation. Now when these pulses of condensation meet in the centre of the tube, that which comes from (b), if it alone were present, would cause the air particles there to move downwards, while that from (a), would move them in the opposite direction. The result, as before will be, that the air particles in the centre will remain at rest; and com­paring these pipes with the strings already studied, we see that under these circumstances, the middle of the tube becomes a "node," while the ends, being places of greatest vibration, corre­spond to the middles of " ventral segments." Further, as the impulses enter an open pipe, and are reflected at the ends, these points must always be places of maximum vibration, that is, must always correspond to the middle of ventral segments. But two ventral segments must necessarily be separated by a node: therefore, the above is the simplest way in which the column of air in an open tube can vibrate, and consequently this form of vibration must give the fundamental tone of the pipe. It may be represented by fig. 54 (A), in which the straight line in the centre shows the