384 THE OVERTONES OF TUBES. 



The overtones of columns of air in tubes are ' har- 

 monic;' that is, their numbers of vibrations are whole 

 multiples of the vibrations of the fundamental note. 

 Tubes which are open at both ends are capable of giving 

 out the whole series of overtones, like vibrating cords 

 (compare page 362) ; tubes closed at one end can only 

 give out those overtones of which the numbers of vibra- 

 tionsmre odd multiples of their fundamental note ; thus,, 

 for c as fundamental note, the overtones </, e', V b, d"\ 

 Between the sounds of two organ-pipes, one open at the 

 end and the other closed (or 'stopped'), there is a differ- 

 ence similar to that between the sounds of two cords, of 

 which one is plucked near the end, and the other near 

 the middle : the sound in the latter case is weaker and 

 more nasal. In general, the overtones of tubes are fainter 

 than those of strings ; the sound of tubes is therefore 

 always much softer than that of strings. Organ -pipes, 

 especially when narrow compared with their length, 

 give out overtones without the fundamental note if they 

 are blown with considerably greater force than is re- 

 quired for the production of the fundamental note ; in 

 open pipes the octave, twelfth, and second octave may 

 in this manner easily be obtained, and in stopped pipes 

 the twelfth, and the third above the second octave. 



In fig. 232 the manner in which the air moves in 

 tubes is pointed out by small arrows ; the perpendicular 

 lines indicate the positions of nodes. In tubes closed at 

 one end there must always be a node at the closed end. 

 A and B exhibit the motion of air for the production of 

 the fundamental note ; C to H show the production of 

 the overtones. 



The rigid parts c f the tube act in those vibrations of 



