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IX. On the Passage of Sound through Narrow Slits. 

 By Lord Rayleigh, O.M., Pres.R.S* 



THEORY leads to the curious conclusion that plane waves 

 o£ sound incident upon a parallel infinitely thin re- 

 flecting screen in which is perforated a narrow slit, are 

 transmitted in a degree depending but little upon the width 

 of the slit. If the plane o£ the screen be at x = 0, and i£ the 

 waves incident on the negative side be denoted by 



^> = cos (lit — hv), ..... (1) 



then the waves diverging from the slit upon the positive 

 side have the expression 



_ _/ it \g cos (nt — h % — \ tr) ._ 



Vp~ \2krJ V+log(ikb) ' * ' ' X] 



in which 26 is the width o£ the slit, r the perpendicular 

 distance of any point from it, Y = Euler's constant ("5772), 

 and as usual k = "2irj\ the wave-length f . These equations 

 apply also to the case of light incident upon a perfectly 

 reflecting screen, provided that the electric vector is per- 

 pendicular to the length of the slit. 



I thought that it would be of interest to examine the 

 question experimentally, but the difficulties in the way have 

 turned out to be more considerable than had been expected. 

 In dealing with sound- vibrations we have a large choice of 

 wave-lengths, down to 1 inch, or less if a sensitive flame be 

 employed as percipient. But, even so, there are formidable 

 obstacles in the way of realizing the theoretical conditions. 

 In practice the screen must be limited ; and then if the 

 source be situated far behind, sound readily passes the 

 boundary, and with the aid of reflexions reaches the ear 

 more effectively by this course than through the slit; while 

 if the source be near, the waves incident upon the slit are 

 not sufficiently plane. Even with the shortest waves an 

 adequate approximation to the infinitely wide and at the 

 same time infinitely thin screen of theory seems unrealizable. 

 An attempt was next made to obviate the difficulty by boxing 

 up the source of sound so as to ensure that nothing could 

 reach the ear otherwise than through the slit. Even this 

 demand is not met without much care, and when it is met 

 there is no security that the amplitude and phase of the 

 vibration at different parts of the length of the slit shall be 

 the same. As to this length itself, it is evident that it ought 



* Communicated by the Author. 



t Phil. Mag. xliii. p. 259 (1897) ; < Scientific Papers/ iv. p. 291. 



