SOUND 



583 



the length of the tube. Hence, if the fundamental 

 tone has frequency 100, the second has frequency 



200, the third 300, 



- " and so on. In the 



:: "- closed or stopped 



'^^ ==! organ -pipe, again, 



one end is a node and 

 the other a loop. In 

 tig. 5, a, we have a 

 diagrammatic repre- 

 sentation of the 

 prime tone, whose 

 wave-length is ( ap- 

 proximately ) four 

 times the length of 

 the tube. Thus by 



X. 



Fig. 4. 



simply stopping the one end of an open organ-pipe 

 we lower the prime tone a whole octave. '1 he next 

 possible mode of vibration is indicated in b ( fig. 5 ), 

 in which are two nodes. Here the wave-length is 

 li times the length of the tuba In the next mode, 

 with three nodes (fig. 5, c), the wave-length is j 



of the length of the 

 tube ; and so on to 

 higher harmonics. 

 If the fundamental 

 tone of a closed pipe 

 has frequency 100, 

 the next possible har- 

 monic will have fre- 

 quency 300, the next 

 500, and so on. Thus 

 in any note uttered 

 by an open pipe all 



...X.. 



the harmonics may 

 ** enter ; but in a closed 



organ-pipe only those 



of odd number can be present. This lack of the 

 even harmonics gives a curious nasal quality to the 

 tone of the closed organ-pipe. By overblowing we 

 may so accentuate the second harmonic in the open 

 pipe as to make it sound a note appreciably an 

 octave higher than the fundamental note. By over- 

 blowing the closed pipe the pitch of the note jumps 

 up an octave and a filth. \\ ith flutes and whistles 

 similar effects may be produced. 



A tuning-fork is a vibrating bar whose one end 

 i a node. In producing its fundamental tone 

 each prong vibrates so that there is no other node, 

 as in fig. 6, a. The next possible mode of vibra- 

 tion is when a second node exists, as shown in 

 fig. 6, b. This first overtone is not related to the 

 fundamental tone according to the harmonic series 

 already given for strings and air columns. For 

 example, if the fundamental 

 tone of the tuning-fork is C 

 of the bass clef, the first over- 

 tone is two octaves and 7 '7736 

 mean semitones higher le. a 

 little flatter than Gjt above 

 the treble C. In the case of 

 stretched membranes, vibrating 

 plates, and bells similar com- 

 plexities hold ; and it is impos- 

 sible to get from them over- 

 6 tones harmonically related to 

 Fig. 6. the fundamental tone and to 



one another. There is no 

 doubt, however, that the characteristic clang of 

 a bell is due to the presence of these aiiYiar- 

 monie overtones ; and the art in bell-making is 

 to prevent them having a pronounced discordant 

 effect on the ear. By careful manipulation the 

 first anharmonic overtone of a large-sized tuning- 

 fork may be made to sound instead of the funda- 

 mental tone, and not infrequently it may be heard 

 along with it. In this latter case it rapidly dies 

 away, and the tuning-fork continues to utter a 



pure tone of the simplest harmonic type. When 

 strings or columns of air are vibrating, the har- 

 monic overtones may be picked out by the ear 

 with tolerable ease after a little practice. Their 

 presence may, however, be made evident to the 

 most unmusical ear by the use of resonators. 



The function of a resonator is to reinforce the 

 intensity of a note produced by some vibrating 

 body in its neighbourhood. The principle is made 

 use of in all musical instruments. For instance, in 

 the violin the greater part of the energy of vibra- 

 tion of the string does not pass directly to the air, 

 but indirectly through the body of the violin, which 

 vibrates with the string. The sounding-board of a 

 piano plays the same role, being set into vibration 

 by the impacts of the waves upon the terminal 

 fixed points of the strings. In these and similar 

 cases a greater mass of air is influenced bv the 

 vibrations of the system, the energy originally 

 given to the string is more quickly transferred to 

 the air, and the result is increased intensity. The 

 word resonator is, strictly speaking, applied to a 

 body which resounds to one note only or to one of 

 a definite harmonic series. If a tuning-fork be 

 held in front of the lip of an organ-pipe, one of 

 whose own harmonics has the same pitch as the 

 note of the tuning-fork, the sound uttered by the 

 tuning-fork will be distinctly reinforced. This 

 reinforcement will not occur in the case of a 

 tuning-fork having no harmonic relation to the 

 pipe. The pipe in the above case acts as a reson- 

 ator. Again, hold down any note on the piano so 

 as to leave the corresponding strings free, and then 

 strike the note an octave lower, or an octave and 

 a fifth, or two octaves lower. Release this latter 

 note, so that its strings become damped, and the 

 former note will be heard distinctly as if it had 

 itself teen struck. Its intensity may be reinforced 

 again and again by repeated striking of a lower 

 note of which it is an harmonic. Here the strings 

 of the note that is being held down act as reson- 

 ators to the corresponding harmonic of the note 

 that is struck. The same effect may be produced 

 by singing a suitable note, or playing it on some 

 other instrument. The boxes to which large 

 tuning-forks are attached are so shaped that the 

 mass of air within them vibrates naturally to the 

 note of the tuning-fork. And just as a pendulum 

 or ordinary swing may be made to describe larger 

 and larger arcs by properly timed impulses, so 

 a resonator responds to the timed pulses of 

 the note to which it is tuned. Helmholtz's 

 spherical resonators, tuned to the successive har- 

 monics of a particular note, are an indispensable 

 part of the equipment of a physical laboratory. 

 Each is a hollow sphere provided with two aper- 

 tures diametrically opposite each other. The 

 smaller aperture is made in the form of a small 

 projecting tube which can be fitted close into the 

 ear. Through the other and larger aperture the 

 outside disturbance sets the mass of air inside the 

 sphere into vibration. As an example of their use, 

 take the case when the note to which one of the 

 resonators is tuned is sounded by ( 1 ) an open organ- 

 pipe, (2) a closed organ-pipe. By placing in turn 

 each resonator to the ear we readily convince our- 

 selves that the successive harmonics are all present 

 in the sound of the open organ-pipe, but that 

 with the closed pipe the even harmonics are absent. 

 When the proper resonator is placed behind a 

 tuning-fork the sound becomes powerfully rein- 

 forced. By taking advantage of this principle 

 Helmholtz proved synthetically that vowel-sounds 

 of the same pitch have ditl'erent harmonics pres- 

 ent. By means of the Phonograph (q.v.) Jenkin 

 and Ewing analysed the vibrations produced by 

 vowel-sounds at various pitches ; and their results 

 show that the relative intensities of the principal 



