is sounding.
When the first overtone is sounded the column divides itself into two vibrating parts. Where will the node between them be? We might naturally say, "Half-way up." But this cannot be so; for if the node were so situated, an impulse going down the pipe would only have to travel to the bottom to find another node, while an impulse going up would have to travel to the top and back again—that is, go twice as far. So the node forms itself one-third of the distance down the pipe. From B to A (Fig. 136, 2) and back is now equal to from B to C. When the second overtone is blown (Fig. 136, 3) a third node forms. The pipe is now divided into five semi-ventral segments. And with each succeeding overtone another node and ventral segment are added.
The law of vibration of a column of air is that the number of vibrations is directly proportional to the number of semi-ventral segments into which the column of air inside the pipe is divided.29 If the fundamental tone gives 100 vibrations per second, the first overtone in a closed pipe must give 300, and the second 500 vibrations.
THE OPEN PIPE.
A pipe open at both ends is capable of emitting a note. But we shall find, if we experiment, that the note of a stopped pipe is an octave lower than that of an open pipe of equal length. This is explained by Fig. 137, 1. The air-column in the pipe (of the same length as that in Fig. 136) divides itself, when an end is blown across, into two equal portions at the node B, the natural point to obtain equilibrium. A pulse will pass from A or