140 VIBRATION OF MUSICAL STRINGS. SECT. XVII. 



SECTION XVII. 



Vibration of Musical Strings Harmonic Sounds Nodes Vibration of 

 Air in Wind-instruments Vibration of Solids Vibrating Plates 

 Bells Harmony Sounding Boards Forced Vibrations Resonance 

 Speaking Machines. 



WHEN the particles of elastic bodies are suddenly disturbed by 

 an impulse, they return to their natural position by a series of 

 isochronous vibrations, whose rapidity, force, and permanency 

 depend upon the elasticity, the form, and the mode of aggrega- 

 tion which unites the particles of the body. These oscillations 

 are communicated to the air, and on account of its elasticity they 

 excite alternate condensations and dilatations in the strata of the 

 fluid nearest to the vibrating body ; from thence they are pro- 

 pagated to a distance. A string or wire stretched between two 

 pins, when drawn aside and suddenly let go, will vibrate till its 

 own rigidity and the resistance of the air reduce it to rest. These 

 oscillations may be rotatory, in every plane, or confined to one 

 plane according as the motion is communicated. In the piano- 

 forte, where the strings are struck by a hammer at one extremity, 

 the vibrations probably consist of a bulge running to and fro 

 from end to end. Different modes of vibration may be obtained 

 from the same sonorous body. Suppose a vibrating string to 

 give the lowest C of the pianoforte which is the fundamental 

 note of the string ; if it be lightly touched exactly in the middle, 

 so as to retain that point at rest, each half will then vibrate twice 

 as fast as the whole, but in opposite directions ; the ventral or 

 bulging segments will be alternately above and below the natural 

 position of the string, and the resulting note will be the octave 

 above C. When a point at a third of the length of the string is 

 kept at rest, the vibrations will be three times as fast as those of 

 the whole string, and will give the twelfth above C. When the 

 point of rest is one-fourth of the whole, the oscillations will be 

 four times as fast as those of the fundamental note, and will give 

 the double octave ; and so on. These acute sounds are called 



