T II IC 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[SIXTH SERIES.] 



SEPTEMBER 190^x^ 





XXXVII. On the Production and Distribution of Soicml, 

 By Lord Rayleigh, O.M., P.R.S., Scientific Adviser to 

 the Trinity IJouse^. 



Theory of Conical Trumpet. 



THE theory o£ small periodic vibrations having their 

 origin at a single point of a gas and thence spreading 

 symmetrically has long been known. The following state- 

 ment is from ' Theory of Sound ' t, § 280. In it a denotes 

 the velocity of sound, and k = 27rlX, X being the wave- 

 length. 



" If the velocity-potential be 



Ave have for the total current crossing a sphere of radius r, 



A7rr^~ =A {cos k{at—r) —krsin k [at — r)\ 

 = A cos kat^ 



when r is small enough. If the maximum rate of introduc- 

 tion of fluid be denoted by A, the corresponding potential 

 is given by (1). 



'' It will be observed that when the source, as measured by 

 A, is finite, the potential and the pressure-variation (pro- 

 .portional to d<l>ldt) are infinite at the pole. But this does 



* Communicated by the Author. 



t MacMillan & Co., first edition 1878, second edition 1896. 



Phil Mag, S. 6. Vol. 6. No. 33. Sept. 1903. U 



