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XXI. On Resonant Reflexion of Sound from a Perforated 

 Wall. By the late Lord Rayleigh, O.M., F.R.S.* 



[This paper, written in 1919, was left by the Author 

 ready for press except that the first two pages were missing. 

 The preliminary sentences, taken from a separate rough 

 sheet, were perhaps meant to be expanded. 



Prof. Wood f had observed highly coloured effects in the 

 reflexion from a granular film of sodium or potassium, 

 which he attributed to resonance from the cavities of 

 a serrated structure of rod-like crystals.] 



THIS investigation was intended to illustrate some points 

 discussed with Prof. R. W. Wood. But it does not 

 seem to have much application to the transverse vibrations 

 of light. Electric resonators could be got from thin con- 

 ducting rods yA, long ; but it would seem that these must be 

 disposed with their lengths perpendicular to the direction 

 of propagation, not apparently leading to any probable 

 structure. 



The case of sound might perhaps be dealt with experi- 

 mentally with bird-call and sensitive flame. A sort of wire 

 brush would be used. 



The investigation follows the same lines as in 'Theory of 

 Sound,' 2nd ed. § 351 (189H), where the effect of porosity 

 of walls on the reflecting power for sound is considered. In 

 the complete absence of dissipative influences, what is not 

 transmitted must be reflected, whatever may be the irregu- 

 larities in the structure of the wall. In the paragraph 

 referred to, the dissipation regarded is that due to gaseous 

 viscosity and heat conduction, both of which causes act with 

 exaggerated power in narrow channels. For the present 

 purpose it seems sufficient to employ a simpler law of 

 dissipation. 



Let us conceive an otherwise continuous wall, presenting 

 a flat face at /e = 0, to be perforated by a great number of 

 similar narrow channels, uniformly distributed, and bounded 

 by surfaces everywhere perpendicular to the face of the 

 wall. If the channels be sufficiently numerous relatively to 

 the wave-length of vibration, the transition, when sound 

 impinges, from simple plane waves on the outside to the 



* Communicated by Sir Joseph Larmor. 



t See Phil. Mag. July 1919, p. 98-112, especially p. Ill, where 

 a verbal opinion of Lord Rayleigh is quoted that in certain cases the 

 grooves of gratings might possiblv act as resonators. 



Phil Mag. S. 6. Vol. 39. No. 230. Feb. 1920. Q 



