Manchester Memoirs, Vol xlii. ( 1 898), No. 0. 



IX. On the Velocity of Sound in a Tube, as affected 

 by the Elasticity of the Walls. 



By Prof. Horace Lamb, M.A., F.R.S. 



Received and read March 8th, iSgS. 



Reference having been made to this subject in the 

 course of a recent discussion in the Society, it occurred 

 to the writer that some results of interest might be 

 obtained without much trouble by applying the known 

 theory of the deformation of a thin cylindrical tube. It 

 soon appeared that although in the case of air-waves in a 

 glass or metal tube the effect would be quite insignificant, 

 yet in the case of such a tube filled with water (or other 

 liquid) the velocity of sound-waves in the fluid might be 

 very appreciably reduced. This had indeed been predicted 

 long ago by Helmholtz,* and assigned by him as the true 

 explanation of the diminution observed in some experi- 

 ments of Wertheim. On further looking into the literature 

 of the subject, the author found that the problem had 

 been treated mathematically by Korteweg in iS/S.f As 

 the investigation given below in § i follows a somewhat 

 different plan, and embraces one or two collateral problems 

 of interest, the writer ventures to submit it to the Society, 

 although on the main question it does little more than 

 confirm the results obtained in the paper cited. 



When the assumption that the thickness of the tube 

 is small compared with the radius is abandoned, the 

 problem becomes much more difficult. The method of 



* Fortschritte der Physik, t. iv. ; Ges. Abh., t. i., p. 246. 

 t Wied. Ann., I. v., p. 526. This paper gives references to the more 

 recent experimental investigations on the subject by Kundt and Dvorak. 



yL^i^th, i8g8. 



