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V. § 58.] REFLEXION AT A CLOSED ORIFICE. 119 |
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will therefore expand. Forward motion being barred by AB, the expansion must take place entirely in the opposite direction. Hence the pulse of condensation is reflected at the end of the pipe, and proceeds to describe its previous course in the reverse direction. Next, suppose CABD to be a pulse of rarefaction. The air in it is at a less pressure than that of the air behind it. As there is a fixed obstacle in front, this rarefaction must be wholly filled up from behind. The condensed air behind will expand more during the process, and become itself more rarefied, than if there had been no obstacle. A rarefied pulse will therefore return along the pipe. Thus a pulse of rarefaction, equally with one of condensation, is reflected at the closed end of the pipe. Neither pulse suffers any other change except in the direction of its motion. Since every pulse is thus regularly reflected at AB, and made to travel back unchanged along the pipe, it follows that a system of equal waves advancing in the direction of the arrow is necessarily met by an exactly equal system proceeding in the opposite direction. For stopped pipes, therefore, the point required to be proved is made out.
Let AB, Fig. 38, be one end of an open pipe, along which condensed and rarefied pulses are being alternately transmitted in the direction of the arrow. |
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