SECT, xvii.] VIBRATION OF A COLUMN OF AIR. 159 



the reeds in Pan's pipes ; over a hole in one side, as in the 

 flute ; or through the aperture called a reed, with a flexible 

 tongue, as in the clarinet, puts the internal 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 un- 

 dulations 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 long as the tube, the second 

 harmonic by waves a third as long, and so on. The har- 

 monic 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 fundamental 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 (K 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 



