24 M. A. Kimdt on the Velocity of Sound in Tubes. 



of the tube by the interposed septum. In very wide tubes an 

 alteration in the velocity of sound when the wall of the tube is 

 altered is everywhere not perceptible. 



(6) The velocity of sound in air is not appreciably dependent 

 on the intensity of the note. 



It follows from these results, that in all those cases in which 

 it cannot be certainly established that the tubes are so wide as 

 not at all to influence the velocity of sound, the value obtained is 

 too small. In all the ordinary musical instruments, the diameter 

 of the sounding columns of air, as compared with the wave-length, 

 is small ; and there must therefore be a diminution of the velocity 

 of sound in all. The attempts to make the observed tones of 

 stopped and of open pipes accord with theory are fruitless, if the 

 velocity of sound in air is taken as a basis and not that in the 

 pipe, which must always be first specially ascertained. 



It has been already observed by Dulong that, apart from all 

 corrections for the ends of tubes, the velocity was found to be too 

 small, though this was not ascribed to the influence of the wall of 

 the tube. 



Two modes of explaining the changes observed in the velocity 

 present themselves : — 



Friction of the air in the tube might first of all diminish the 

 velocity of sound. But it has already been proved elsewhere 

 that the internal friction of air cannot diminish the velocity of 

 sound in the open air; and from several reasons it is probable 

 that in a tube (in which, certainly, the density of air increases 

 towards the sides) the amplitude, but not the velocity, may be 

 altered by friction. It is true that the friction in a tube has not 

 been demonstrated to be without influence on the velocity. 



Yet the origin of the discrepancies observed may probably be 



sought in an exchange of heat which takes place between the air 



which propagates the sound and the wall of the enveloping tube. 



Since part of the heat produced in the motion of sound is given 



to the wall, and an equal part of that consumed at another instant 



is replaced by the wall, the produced and consumed heat are not 



entirely used, as Laplace assumes, for the acceleration of sound. 



Hence the velocity of sound must be smaller. The factor which 



Laplace introduces into the formula no longer corresponds to 



c 

 — = 1-41, but, inasmuch as heat is exchanged, is smaller. If 



c \ 



all the produced and consumed heat were imparted and restored, 

 we should have k = l; that is, the velocity would sink from 

 332*8 to 280 metres, Newton's value. A diminution of one- 

 half is in fact evident from the Table. 



Since all the circumstances which increase the surface of the 

 sounding column of air, as compared with its volume, favour an 



