SECT. XVII. VIBRATION OF A COLUMN OF AIR. 137 



as in the flute ; or through the aperture called a reed 

 with a flexible tongue, as in the clarinet, puts the inter- 

 nal column of air into longitudinal vibrations by the 

 alternate condensations and rarefactions of its particles. 

 At the same time the column spontaneously divides 

 itself into nodes between which the air also vibrates 

 longitudinally, but with a rapidity inversely proportional 

 to the length of the divisions, giving the fundamental 

 note or one of its harmonics. The nodes are produced 

 on the principle of interferences by the reflection of the 

 longitudinal undulations of the air at the ends of the 

 pipe, as in the musical string, only that in one case the 

 undulations are longitudinal, and in the other transverse. 

 A pipe either open or shut at both ends when 

 sounded vibrates entire, or divides itself spontaneously 

 into two, three, four, &c. segments separated by nodes. 

 The whole column gives the fundamental note by 

 waves or vibrations of the same length with the pipe. 

 The first harmonic is produced by waves half as lon as 

 the tube, the second harmonic by waves a third as long, 

 and so on. Th^ harmonic segments in an open and 

 shut pipe are the same in number, but differently 

 placed. In a shut pipe the two ends are nodes, but in 

 an open pipe there is half a segment at each extremity, 

 because the air at these points is neither rarefied nor 

 condensed, being in contact with that which is external. 

 If one of the ends of the open pipe be closed, its funda- 

 mental note will be an octave lower, the air will now 

 divide itself into three, five, seven, &c. segments ; and 

 the wave producing its fundamental note will be twice 

 as long as the pipe, so that it will be doubled back 

 (X. 177). All these notes may be produced separately, 

 by varying the intensity of the blast. Blowing steadily 

 and gently, the fundamental note will sound ; when the 

 force of the blast is increased, the note will all at once 

 start up an octave ; when the intensity of the wind is 

 augmented, the twelfth will be heard, and by continuing 

 to increase the force of the blast the other harmonics 

 may be obtained, but no force of wind will produce a 

 note intermediate between these. The harmonics of a 

 flute may be obtained in this manner, from the lowest 

 C or D upward, without altering the fingering, merely 

 M 2 



