EAR AS AN ORGAN FOR SOUND SENSATIONS. 



393 



at the same time the actual movement of the molecules will be a 

 resultant of the forces acting upon them at any given instant, and 

 will be indicated, therefore, by the algebraical sum of the ordinates 

 above and below the lines of rest. If the movements are so timed 

 that e in curve B is synchronous with d° in curve A, then the 

 resulting compound wave form is illustrated by C. If, how- 

 ever, curve B is supposed to be in a different phase, so that e 

 is synchronous with d', then a form of wave illustrated by D will be 

 obtained. In this way a great variety of forms of compound waves 

 may be supposed to be produced by the union of a series of simple 

 waves of different periods of vibration. That compound waves dif- 

 fer from simple ones in being composed of several series of vibrations 

 is indicated directly by our sensations. When we listen to the note 

 of a tuning-fork we hear only a single tone; when two or more 

 tuning-forks are sounded together the trained ear can detect the tone 

 due to each fork, and similarly when a single note is sounded by 

 the human voice, a violin, or any other instrument that has a char- 

 acteristic quality the trained ear can detect a series of higher tones, 



Fig. 175. — Schema by Helmholtz to illustrate the formation of a compound wa-'e 

 from two pendular waves: A and B, pendular vibrations, B being the octave oi A. If 

 superposed so that e coincides with d° and the ordinates are added algebraically, the non- 

 pendular curve C is produced. If superposed so that e coincides with d' the non-pendular 

 curve D is produced. 



the upper partial tones, or harmonics, or overtones, which indicate 

 that the note is really compound, and not simple. The formation 

 of these overtones is due to the fact that the sounding body may be 

 considered as vibrating not only as a whole, but also in its aliquot 



