THE VIBRATIONS OF GASEOUS BODIES. 375 



e overtones of plates, bells, and rods are not har- 

 monic tones; that is, their numbers of vibrations do not 

 bear the simple ratios to the fundamental note that the 

 overtones of strings do. The overtones do not form con- 

 sonant combinations with the fundamental note, and 

 hence these bodies are employed only in a very limited 

 degree in music. 



Gaseous bodies are capable of performing regular 

 vibratory movements if they are enclosed in vessels with 

 one or more apertures. Tubular vessels are especially 

 Adapted for musical purposes. The height of the note 

 : produced depends essentially on the length of the vibra- 

 ting column of air; that is, on the length of the tube. 

 The vibrations of the particles of air resemble those 

 ,by means of which sound is _ . __ 



propagated in air ; that is, they i ! I L__LLj, _!._, 



ire longitudinal vibrations, ^ , 

 but the wave produced is ' J 

 termed a stationary wave in ^ ; ', ! 

 opposition to a progressive *~ L ~"~~ 



wave. Fi. 226 serves to show 



the kind of motion which gives rise to a stationary 

 'In a progressive wave (compare figs. 209 and 210) all 

 particles of air describe equal spaces, but each particle 

 begins and ends its motion an instant later than the 

 (preceding one ; in a stationary wave, on the other hand, 

 ill particles begin and end their motion at the same 

 instant, but the different particles pass through unequal 

 spaces while moving to and fro. Fig. 226 represents 

 i tube open at both ends, and the short vertical lines 

 ire supposed to be particles of air, equally distant from 

 one another when the air is at rest ; this is the state 



