376 



THE POPULAR EDUCATOR. 



ACOUSTICS. Y. 



MUSICAL PIPES VIBRATION OF AIR IN TUBES THE HUMAN 



VOICE SYMPATHETIC FLAMES THE MUSICAL SCALE 



CHORDS AND DISCORDS STRUCTURE OF THE EAR. 



IN our last lesson we inquired into the manner in which cords 

 and plates may be made to vibrate, and thus produce musical 

 notes. There are, however, many musical instruments in which 

 the sound is produced by the column of air contained in a tube 

 being thrown into vibration ; these are usually distinguished as 

 wind instruments, and the organ-pipe may be taken as the type 

 of the class. 



We have already seen that by holding any tuning-fork to 

 the mouth of a glass jar, of suitable length, the sound will be 

 greatly increased by resonance. Now remove the tuning-fork, 

 and, holding the tube to the lips, blow across its open mouth, 

 a note will be produced which will be found to bo exactly the 

 same as that of the tuning-fork. The rush of the air across the 

 open mouth causes a number of different pulses, of which the tube 

 selects the one which is in most perfect accordance with itself, 

 and increases its power. By taking different tubes, and blowing 

 across them in this way, we shall find that in each case exactly 

 the same note is produced as that uttered by a tuning-fork 

 which resounds with the tube. 



By blowing more violently we shall obtain a note considerably 

 above that first heard, and by blowing with still greater force 

 we shall obtain notes successively higher and higher. If the 

 number of vibrations corresponding to the fundamental note be 



represented by 1, we 

 shall find that these 

 overtones, as they are 

 called, are represented 

 m by the odd numbers 

 3, 5, 7, etc. If, for 

 instance, the funda- 

 mental note requires 

 100 vibrations in a 

 second, the next note 

 above it that can bo 

 obtained from the 

 same pipe is produced 



A B C by 300 vibrations in 



Fig. 20. the same time. We 



cannot make the pipe 



utter any intermediate note, as, for instance, one with 200 or 

 250 vibrations. 



By examining the condition of the air inside the tube, we 

 shall be able to understand the reason of this. We shall find 

 that the bottom of the tube is always a node, while the mouth 

 corresponds to a ventral segment. 



When the fundamental note is sounded, the length of the 

 sound-wave is just double that of the tube ; the motion of the 

 air in which is represented at A (Fig. 20), being merely a single 

 pulse up and down. 



Now, as we blow more violently, a node is formed in the tube, 

 and since the mouth is a ventral segment and the bottom a 

 node, the second node must clearly be one-third of the way down 

 the tube, as shown at a. The pulses in this case will be as 

 represented in the above figure at B. The node a may indeed 

 be considered as a thin layer of air remaining quite motionless, 

 whilo the air between it and the next node, which in the case 

 under consideration is the bottom of the tube, pulses alter- 

 nately backward and forward. 



A very good proof of this statement is afforded by placing an 

 Organ-pipe on a wind-chest, and procuring a small membrane 

 stretched over a ring of such a size as to be capable of passing 

 np and down the tube, which, for this experiment, should have 

 a glass side. This membrane is then suspended horizontally 

 by strings, and lowered down the tube. It will be seen that at 

 some parts it is thrown into rapid vibration, while in other 

 places it will be at rest. This will be rendered more manifest 

 by sprinkling some fine sand on it before lowering it into the 

 ^fi' c Bj watcnin the P lace at which the vibrations cease, we 

 shall find that it is just when the membrane is at one of the 

 nodes, thus clearly showing that there the air is at rest. 



When we blow more violently across the tube, two nodes will 

 be produced, as seen at c ; and in this case it is clear that the 

 waves produced can only be one-fifth the length of those pro- 



Fig. 21. 



duced when the whole pipe sounds, as at A. The number of 

 vibrations is therefore five times as great. 



Thus far we have employed pipes closed at one end. If now 

 we take others, similar in every other respect, but open at both 

 ends, we shall find that the notes produced are just an octave 

 higher, that is, an open tube yields a note an octave higher 

 than a similar closed one of the same 

 length. The different notes produced 

 by an open tube may be represented 

 by the successive numbers 1, 2, 3, 4, 5, 

 etc. In all cases the extremities are 

 ventral segments, and the nodes are 

 distributed evenly between them. 



We have now to see the way in 

 which pipes are employed in musical 

 instruments. The common Pan pipe 

 consists merely of a series of open 

 tubes sounded by the mouth. In musi- 

 cal instruments, however, there is 

 nearly always some special form given 

 to the mouthpiece, which modulates 

 to a greater or less extent the peculiar 

 sound of the pipe. Fig. 21 shows the 

 usual construction of the mouthpieces 

 of the flageolet and of the organ- 

 pipe. The end p of the latter is inserted in the wind-chest 

 of the organ, whence the air issues into a cavity, i, which is 

 frequently of larger dimensions than represented in the figure. 

 As this issues from i, the current strikes against the upper lip 

 6, and produces pulsations ; these, by the resonance of the pipe, 

 yield the required musical note, the pitch of which depends 

 chiefly upon the length and size of the pipe. 



In an organ the same pipe always utters the same note, the 

 different sounds being produced by a corresponding number of 

 pipes. In other instruments as, for example, the flute, trumpet, 

 and cornet-a-piston many notes may bo produced from the same 

 tube. This is accomplished partly by altering the position of 

 the lips, or the intensity of the blast, and partly by altering the 

 virtual length of the tubes by means of apertures or stops. 



In the flute there are a number of openings, which are kept 

 closed by the fingers. When any one of these is left unstopped, 

 a ventral segment is produced in the tube at that point, and, 

 modifies the note. The vibrations in this instrument are pro- 

 duced by the current of air 

 from the lips being directed 

 over an aperture in the side 

 of the tube. 



In reed-pipes the vibra- 

 tions are more or less con- 

 trolled by means of a vibrat- 

 ing metal tongue, somewhat ^* 

 similar to that employed in 

 an harmonium. A pipe of 

 this nature, fitted with a 

 piece of glass, so as to ex- 

 hibit the reed, is shown in 

 Fig. 22. Q is the wind-chest 

 of the bellows, into which P 

 is fitted. In the right-hand 

 figure the upper part of the 

 pipe is removed, so as to 

 show the reed more clearly. 

 A plate of metal, c c, has a 

 slit cut in it, in which the 

 tongue may just pass. When 

 the air issues through the 

 tube this tongue is thrown 

 into vibration, and regulates 

 the pulsations in the tube. 

 By means of a curved wire, 

 r, projecting above the top 

 of the pipe, the play of the 



tongue may be controlled and the pipe tuned. The conical pipe, 

 H, placed at the top, serves to increase the power of the sound. 



The organ of voice is, in reality, a reed instrument of the 

 most perfect construction. It is situated at the upper end of 

 the windpipe, which is nearly closed by certain elastic bands 

 and membranes. When the air is forced betwoen these they are 



