Lord Rayleigh on the Theory of Resonators. 421 



Chapter IV.* Let A be a simple source of sound at a distance 

 from the mouth of the pipe. We know that at a point B (not 

 too near the mouth) whose distance from the closed end is ex- 

 actly -, there is no variation of density. From this it follows, 



by the principle, that, if B 

 were made a source of 

 sound, there would be no 

 variation of density at A — 

 that is to say, that sound 

 originating in B could not 

 find its way out of the 

 pipe. The restriction pre- 

 cluding too great a proxi- 

 mity to the mouth may 

 be removed, if we suppose 

 the source B to be uni- 

 formly diffused over any 

 cross section of the pipe 



(distant - from the closed 



13 



end) instead of concentrated in one point. Here again the reso- 

 nator may be said to absorb sound that would otherwise diffuse 

 itself in surrounding space ; or, if the non-emission of energy 

 be thought incompatible with the existence of sound, we may say 

 that the effect of the resonator is to dry up the source. For 

 the present purpose it will be most convenient to use the ex- 

 pression " source of sound " in the sense of Chapter VIII., im- 

 plying a given periodic production or abstraction of fluid, or 

 something equivalent in its effect thereto, whether there be or be 

 not emission of energy. The latter case will occur when there is 

 on the whole no variation of pressure at the source itself. 



We see then that, as far as external space is concerned, the 

 neighbourhood of a resonator, far from augmenting the effect of 

 a source, annuls it altogether, by absorbing the condensations 

 and rarefactions into itself. The resonator acts, in fact, in the 

 same way as would an equal and opposite source in the same 

 position. 



The principle here laid down, paradoxical as it will seem to 

 many, is illustrated by the action of very simple apparatus, such 

 as that employed by Quincke and others to stop sound of a par- 

 ticular pitch. Two varieties (figs. 1 and 2) are represented in 



* See a paper by the author, " On some General Theorems relating to 

 Vibrations," Proceedings of the Mathematical Society, June 1873. 



