It Is usual first to give the theory of it closed pipe, and then to suppose the open pipe made of two'olosed pipes, with their closed ends together, and their closing diaphragms removed. The opposition of the vibrating movements will then keep the particles in the middle at rest. This is a sufficient explanation of those modes of vibration of the open pipe in which there is a node in the middle.
We now come to the explanation of the manner in which the sonorous vibration of a pipe is maintained. If we suppose a vibrating body placed at the orifice, it is found that if the vibrations of the body be equal or nearly equal to those of the fundamental note of the tube in the preceding theory, or one of its harmonics, the sound of the vibrating body is reinforced by the tube. A slight alteration of the tube, though it may sharpen or flatten the note, does net by any means produce such a difference as would be caused by the same alteration, if the sound were caused by the tube alone. We do not Intend to go into this subject; the reader may find it discussed, both mathematically and experimentally, in a paper by Mr. Hopkins, published iu tho fifth volume of the ' Transautions of the Cambridge Philosophical Society.' When the sound is caused by a current of air, as in the common flute or simple organ pipe, a tolerably satisfactory explanation of the phenomena has been given in the case of the pipe closed at one end (to which writers have confined themselves); but none whatever in that of the pipe which is open at both ends. In the former case, as in a reed of the Pan's pipe, a current of air Is directed laterally over the mouth of the pipe, with a slight obliquity of direction. A condensa
tion Is therefore produced in the tube, which travels to the closed end, and is there reflected; so that by the time the condensation has travelled over twice the length of the tube (down and back again), the whole condensation, such as it was when it began, is doubled. Hence the air in the tube has now become more powerful than the external stream, and the condensed portion begins to be discharged. This continues until not only the whole of the condensation is discharged, but also until all the velocity of the issuing particles has been destroyed; and this is not done until the effect of that velocity has produced a rarefaction In the tube. The effect of the condensation is destroyed in the same time as that in which it was prodnced; and hence the corn `fete undulation belonging to the whole length of the closed tube is four times the length of the tube. Imrerfect as the preceding explanation is, we know of no way of applying even so much to the open tube.
It is also to be noted that the whole of the preceding theory is but an approximation. The extremities of the open tube are not points of absolute non-condensation and non-rarefaction, but points at which the condensations and rarefactions are least and small. Similarly the nodes are not points in which the air I. absolutely at rest, but points at which the motion is least. The extensions of this theory, however, important as they are in a kihyaical point of view, are not essential to that (undo mental explanation of the musical phenomena of a pipe, to which we have expressed our intention of confining ourselves in the present article.