PIPES AND RESONATORS 277 



pipe are practically dissipated in a fraction of a second ; this is 

 owing to the small inertia as compared with that of a piano- 

 wire. For musical purposes some device for sustaining the 

 note is required. In the ordinary " flute pipe," 

 the lower part of which is shewn in section in 

 Fig. 84, a thin stream of air is driven by pressure 

 from a wind-chest so as to strike against the 

 bevelled lip of the aperture. Under these cir- 

 cumstances a very slight cause will make the jet 

 pass either wholly inside or wholly outside the 

 pipe. The precise mode of action is obscure, but 

 there can hardly be any doubt that in its main 

 features it is analogous to that of a clock-escape- 

 ment. Periodic impulses are given by the jet, 

 alternately inwards and outwards, to the air near 

 the mouth, always in the direction in which the 

 air is tending ; whilst the vibrating column itself 

 mainly determines the epochs at which these impulses shall 

 occur. The circumstances are accurately periodic, so that 

 the driving force can be resolved by Fourier's theorem into 

 a series of harmonic components whose frequencies are as 

 1, 2, 3, .... The relative amplitudes with which these are 

 reproduced in the vibrating column will depend on the 

 closeness of their frequencies to the natural frequencies. Thus 

 in a " closed " pipe, i.e. one closed at the upper end, the 

 harmonics of odd order are alone excited. Again the theory 

 of 87 indicates that in a sufficiently wide pipe the natural 

 frequencies may deviate sensibly from the harmonic relation, 

 in which case only the lower harmonics (after the funda- 

 mental) will be sensible; in particular, a wide closed pipe 

 gives almost a pure tone. On the other hand a pipe which is 

 narrow in comparison with the length may give a note rich in 

 harmonics. Indeed, if such a pipe be blown with sufficient 

 force, the fundamental is not sounded at all, the period becoming 

 that of the first harmonic; if the strength of the blast be 

 further increased the note may jump to the next member of 

 the series, and so on. An explanation is probably to be found 

 in the sort of dynamical elasticity possessed by the jet. 



