Part 18 (1/2)

Chapter XV

WIND INSTRUMENTS

Longitudinal vibration--Coluth and tone--The open pipe--The overtones of an open pipe--Where overtones are used--The arrangement of the pipes and pedals--Separate sound-boards--Varieties of stops--Tuning pipes and reeds--The bellows--Electric and pneuan in the world--Hued instruments we are concerned only with the transverse vibrations of a string--that is, its les to the axis of the string A string can also vibrate longitudinally--that is, in the direction of its axis--asa violin string In this case the harmonics ”step up” at the same rate as when the movements were transverse

Let us substitute for a wire a stout bar of itudinal vibrations of this rod contain overtones of a different ratio The first harmonic is not an octave, but a twelfth While a tensioned string is divided by nodes into two, three, four, five, six, etc, parts, a rod fixed at one end only is capable of producing only those harmonics which correspond to division into three, five, seven, nine, etc, parts Therefore a free-end rod and a wire of the same fundamental note would not have the sa to the difference in the harmonics

COLUMNS OF AIR

In wind instruments we employ, instead of rods or wires, colu th

In the ”penny whistle,” flute, clarionet, and piccolo the length of the colu apertures in the substance encircling the column

RESONANCE OF COLUMNS OF AIR

Why does a tube closed at one end, such as the shank of a key, emit a note e 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, so e 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 audiblehow the har 136, _1_ is a pipe, closed at the botto-fork of the same note as the pipe is struck and held over it so that the prongs vibrate upwards and doards At the cos the air in front of them is _compressed_

This impulse, imparted to the air in the pipe, runs down the column, strikes the bottoinning toa _rarefaction_ of the air behind it This effect also travels down and back up the colu just as it arrives at the furthest point of the inward motion The process is repeated, and the colu atreatly increases the volu-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 Noe blow across the end, we present, as it were, a nu-forks to the pipe, which picks out those air-pulses hich 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 eher 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 thes, are associated the _overtones_, or har 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 fundaot the upper hand

We -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 fro 136, _1_, there is only one point of rest for an impulse--namely, at the bottom of the pipe So that to pass froain The distance froment_ Remember this ter

When the first overtone is sounded the colu parts Where will the node between theht naturally say, ”Half-way up” But this cannot be so; for if the node were so situated, an i down the pipe would only have to travel to the botto 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 Fro 136, _2_) and back is now equal to fro 136, _3_) a third node for 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 numents into which the column of air inside the pipe is divided[29] If the fundaives 100 vibrations per second, the first overtone in a closed pipe ive 300, and the second 500 vibrations

THE OPEN PIPE

A pipe open at both ends is capable of e 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-colu 136) divides itself, when an end is blown across, into two equal portions at the node B, the natural point to obtain equilibriuain in half the ti 136, _1_; therefore the note is an octave higher

[Illustration: FIG 137--Showing how harmonics of an open pipe are formed, B, B1, and C are ”nodes” The arrows indicate the distance travelled by a sound impulse from a node to a node]

THE OVERTONES OF AN OPEN PIPE

The first overtone results when nodes forth of the pipe froments The vibrations now are twice as rapid as before The second overtone requires three nodes, as in Fig 137, _3_ The rate has now trebled So that, while the overtones of a closed pipe rise in the ratio 1, 3, 5, 7, etc, those of an open pipe rise in the proportion 1, 2, 3, 4, etc