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122 VIBRATION-FORMS FOR A STOPPED PIPE. [V. § 59.
densation, so that the wave returns hind part foremost.
59. We will now examine what forms of segmental vibration the air in a stopped pipe can adopt. Every such form must necessarily have a node coincident with the closed end of the pipe, since no longitudinal vibrations are possible there. The impulses constituting the series of direct waves are not, as we shall see presently, originated, like those of a pianoforte string, at some intermediate point, but enter the pipe at its open end. This must therefore be a point of maximum vibration. Now a glance at Fig. 35, shows that the maxima of vibration are at the middle points of the ventral segments. Hence the centre of a segment must coincide with the open end of the pipe.
The above considerations suffice to solve the problem before us. If the closed end of the pipe is placed at A, Fig. 35(1), the open end must be midway between .A and 1, or between 1 and 2, 2 and 3, 3 and 4, and so on. No other forms of vibration are possible.
Fig. 39 shows the air in a stopped pipe of given length vibrating in four such ways. The vertical lines indicate the positions of the nodes. For the sake of greater clearness, the loops of the associated vibration-forms are in each case drawn in dotted lines.