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420 Lord Rayleigh on the Theory of Resonators . 



from a theoretical point of view, more important than the cases 

 in which the rule holds good. Indeed I should prefer to reverse 

 the statement, and say that the neighbourhood of a resonator in 

 unison with a sounding body diminishes the loudness thereof. 



As the subject is rather a delicate one, we will begin by sim- 

 plifying the conditions as much as possible. Let us suppose 

 that the source of sound is a piston, A, imbedded in an infinite 

 rigid plate. In the neighbourhood of A is 

 another piston, B, backed by a spring, whose 

 natural period is exactly the same as that of 

 the vibration imposed upon A. ED is a 

 rigid surface, enclosing A and B, and only 

 allowing the communication of motion to 

 the external atmosphere by means of a mo- 

 vable piston, C. The space enclosed by this 

 surface is supposed to be occupied by gas 

 devoid of inertia. It is easy to see that under 

 these circumstances the piston C, though 

 free to move, would yet remain at rest. For 

 if the pressure within the vessel D E were 

 in truth variable, the piston B would be 

 acted upon by a force whose period was in 

 exact agreement with that natural to itself, 

 and its amplitude of vibration would in- 

 crease without limit. The actual motion of 

 B must be such as to leave the capacity of 

 the vessel and the pressure constant; and 

 then there is no force tending to move C, or rather to keep up 

 the motion of C in the face of the dissipation which would be 

 the necessary consequence of such motion. We may express 

 this effect by saying that the condensations and rarefactions 

 emitted by A are absorbed by B ; and since if B were fixed, C 

 would certainly move on account of the variation of pressure 

 behind it, we see that the effect of the resonator is not to aug- 

 ment the sound, but, on the contrary, absolutely to stop it. 



This conclusion does not depend on the rather artificial cir- 

 cumstances that we have here imagined. If the rigid walls 

 represented by D E be removed, the same argument still shows 

 that the pressure in the space surrounding A B must be inva- 

 riable ; and even if the inertia of the gas be restored, the general 

 result will not be disturbed, provided that the distance A B is 

 only a very small fraction of the wave-length, and that allowance 

 is made for the inertia of the air in the neighbourhood of B in 

 estimating the natural pitch of the resonator. 



An instructive view of this question may also be obtained by 

 means of the general principle of reciprocity established in 



