Why does a tube closed at one end, such as the shank of a key, emit a note when we blow across the open end? The act of blowing drives a thin sheet of air against the edge of the tube and causes it to vibrate. The vibrations are confused, some "pulses" occurring more frequently than others. If we blew against the edge of a knife or a piece of wood, we should hear nothing but a hiss. But when, as in the case which we are considering, there is a partly-enclosed column of air close to the pulses, this selects those pulses which correspond to its natural period of vibration, and augments them to a sustained and very audible musical sound.
Fig 136.—Showing how the harmonics of a "stopped" pipe are formed.
In Fig. 136, 1 is a pipe, closed at the bottom and open at the top. A tuning-fork of the same note as the pipe is struck and held over it so that the prongs vibrate upwards and downwards. At the commencement of an outward movement of the prongs the air in front of them is compressed. This impulse, imparted to the air in the pipe, runs down the column, strikes the bottom, and returns. Just as it reaches the top the prong is beginning to move inwards, causing a rarefaction of the air behind it. This effect also travels down and back up the column of air in the pipe, reaching the prong just as it arrives at the furthest point of the inward motion. The process is repeated, and the column of air in the pipe, striking on the surrounding atmosphere at regular intervals, greatly increases the volume of sound. We must observe that if the tuning-fork were of too high or too low a note for the column of air to move in perfect sympathy with it, this increase of sound would not result. Now, when we blow across the end, we present, as it were, a number of vibrating tuning-forks to the pipe, which picks out those air-pulses with which it sympathizes.
LENGTH AND TONE.
The rate of vibration is found to be inversely proportional to the length of the pipe. Thus, the vibrations of a two-foot pipe are twice as rapid as those of a four-foot pipe, and the note emitted by the former is an octave higher than that of the latter. A one-foot pipe gives a note an octave higher still. We are here speaking of the fundamental tones of the pipes. With them, as in the case of strings, are associated the overtones, or harmonics, which can be brought into prominence by increasing the pressure of the blast at the top of the pipe. Blow very hard on your key, and the note suddenly changes to one much shriller. It is the twelfth of the fundamental, of which it has completely got the upper hand.
We must now put on our thinking-caps and try to understand how this comes about. First, let us note that the vibration of a body (in this case a column of air) means a motion from a point of rest to a point of rest, or from node to node. In the air-column in Fig. 136, 1, there is only one point of rest for an impulse—namely, at the bottom of the pipe. So that to pass from node to node the impulse must pass up the pipe and down again. The distance from node to node in a vibrating body is called a ventral segment. Remember this term. Therefore the pipe represents a semi-ventral segment when the fundamental note 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.