Tones of Overblown Organ Pipes. 77 



phenomenon in the special characteristics of the air-jet in 

 relation to the natural frequencies of vibration of the air 

 enclosed in the pipe. Unlike the bow, the air-jet has,, 

 as we have seen above, certain periodic tendencies of its own 

 arising from the formation of vortices. It has been observed 

 by Wachsmuth * that the excitation of the pipe cannot be 

 maintained steadily unless the lip of the pipe is beyond the 

 breaking-up stage of the jet, and then only when the pitch 

 of the edge-tones approximates to that of the pipe. If so, 

 we may suppose the initiation of the vibration in the pipe to 

 be due to the deflexion of the jet by vortex reaction, its 

 maintenance to the controlling of the deflexions by the 

 combined effect of the pulsations of the air-column and of 

 the vortices forcing each other into step. 



Then, if by raising the wind-pressure the frequency of the 

 vortex pulsations tends to rise and finally breaks out of 

 step, leaving the pulsations of the air-column to control the 

 deflexions of the air-jet, though weakened by the discordance, 

 the quicker vortex pulsations might act independently to 

 excite that mode of vibration of the air-column corresponding 

 to its next higher free period, which would be nearly but not 

 quite the octave. In this way we should have virtually two 

 independent generators, each exciting a composite forced 

 tone consisting of harmonic partials but slightly out of tune 

 with each other. This state of affairs would continue until 

 the rise of pressure brought the frequency of the vortex 

 pulsations into approximate agreement with the octave 

 pitch, when the pipe would again give a steady tone at the 

 higher pitch. It maybe noted that on the above assumption 

 the frequency of the beats would approximate to the difference 

 between the frequencies of the natural and the harmonic 

 overtones, and would remain nearly constant during the 

 whole range of pressure, as seems to be the case in practice. 

 Direct observation of the behaviour of the air-jet may be 

 expected to furnish a test of the correctness of the sugges- 

 tions made above. It is proposed at an early opportunity 

 to undertake the experimental work necessary for this, 

 purpose. 



In conclusion, the author wishes to express his cordial 

 thanks to Prof. 0. V. Raman, in whose laboratory and at 

 whose suggestion this investigation was carried out, for the- 

 facilities placed at his disposal. 



University College of Science, Calcutta, 

 May 3rd, 1921. 



* Loc. cit. 



