CHAPTER V. 



THE COMPRESSION OF A SOUND-WAVE IN DIAPASON PIPES. 



39. Introductory. Lord Rayleigh and, more recently, Prof. A. G. Webster 

 and his students have given considerable attention to this problem. The 

 following experiment is, I think, capable of exact development. 



40. Apparatus. Many years ago * I showed that displacement inter- 

 ferometry lent itself favorably to the study of adiabatic expansion, and this is 

 particularly the case when the achromatic fringes are used. It is therefore 

 suggested f that the endeavor to look with the interferometer through the nodes 

 of an organ-pipe might be successful. 



Open pipes P, adapted for the purpose in question, are shown in figures 67 

 and 68. In figure 67, cylindrical adjutages pp', of somewhat smaller diameter 

 than the pipe (open within, but closed by glass plates gg on the outside), are in- 

 troduced at the node N symmetrically and at right angles to the pipe. The effect 

 of this is to lower the pitch to a degree increasing with the length of p. lip is 

 not too long, one may argue that the resilience of air at the node is decreased, 

 and the period lengthened much in the same way in which an increased capacity 

 operates in an electric circuit. In my case the fundamental pitch was de- 

 pressed about a fourth. The first overtone, however, occurred at about a 

 tenth above this and came out very shrilly, probably because it coincided with 

 the octave of the unchanged pipe. Moreover, this first overtone is prob- 

 ably the fundamental of the small pipes p, p'. Thus, here also, two nodes of 

 the same kind, both compressed and both rarefied, are present and the optic 

 effects (ray L) are correspondingly intense. 



The other form of pipe (shown in fig. 68) has the plane of the embouchure 

 at right angles to the axis of the pipe, which is closed at g by a knife-edged 

 glass plate. The other end may be open, or also closed with glass. The 

 path of the interferometer beam is shown at L. Since the distribution of 

 density is simple harmonic, the details are here quite open to computation. 



Another available pipe is simply an open tube to be excited by resonance. 

 This case is in a measure the most interesting of the three. 



* Carnegie Inst. Wash. Pub. No. 149, 1912. 



t After I had published my note on the present subject in Science (LII, 1920, pp. 586-588), 

 my attention was called, through the kindness of Professors A. T. Jones and H. F. Stimson, 

 to the admirable paper of Raps in the Annalen der Physik (vol. 50, p. 193, 1893) , which had 

 unfortunately escaped me. Raps used the Jamin interferometer, which is less flexible and 

 convenient than the method of the text, the latter permitting the examination of two recip- 

 rocal modes at once. My work, however, has thus been largely anteceded, and I will there- 

 fore give only as much as bears directly on the experiments of the present report. The paper 

 of Topler and Boltzmann (Pogg. Annalen, vol. 141, 321, 1870), using the Fresnel inter- 

 ferometer for the purpose in question, was also pointed out to me by Professor Stimson, but 

 it is less closely connected with the above text. Stimson has used an adaptation of the 

 Chamberlain interferometer. 

 46 



