PHYSICS OF SOUND 



729 



which latter will be described hereafter, can be demonstrated, without 

 damping the strings, by resonators. It is well known that if a glass 

 tube, closed at one end, which contains a column of air of a certain 

 length, is brought near a resounding body emitting a note identical with 

 that produced by the vibrations of the column of air, the air in the tube 

 will resound in consonance with the note, while no other note will have 

 this effect. The resonators of Helmholtz are constructed on this prin- 

 ciple. A glass globe or tube (Fig. 189) is constructed so as to produce 

 a certain note. This has a larger opening (a) and a smaller opening (b), 

 which latter is fitted in the ear with warm sealing-wax, the other ear 

 being closed. When the proper note is sounded, it is reenforced by the 

 resonator and is greatly increased in intensity, while all other notes are 

 heard very faintly. By using resonators graduated to the musical scale, 

 it is easy to analyze a note 

 and distinguish its over- 

 tones. The resonators of 

 Helmholtz that are open 

 at the larger extremity are 

 more delicate than those 

 in which this is closed with 

 a membrane. 



A striking and instruc- 

 tive point in the present 

 discussion is the follow- 

 ing : All the overtones are 

 produced by vibrations of 



divisions Of the String in- 



eluded between the comparatively still points, called nodes; and if 

 a string is thrown into vibration by plucking or striking it at one of 

 these nodal points, the overtones which vibrate from this node at a 

 fixed point are abolished. It is readily understood that when a string 

 is plucked at any point, it will vibrate so vigorously at this point that no 

 node can be formed. This fact has long been recognized by practical 

 musicians, although many probably are unacquainted with its explana- 

 tion. Performers on stringed instruments habitually attack the strings 

 near one of their extremities. In the piano, where the strings may be 

 struck at almost any point, the hammers are placed at a distance of \ 

 to \ of the length of the strings from their extremities ; and it has been 

 ascertained by experience that this gives the richest notes. The nodes 

 formed at these points would produce the /ths and 9ths as overtones, 

 which do not belong to the perfect major chord, while the nodes for the 

 harmonious overtones are undisturbed. The reason, then, why the 



- Resonators of Helmholtz. 



