TRANSACTIONS OF SECTION A. 57S 



An Attempt at n Quantitative Theory of the Telephone.^ 

 By Lord Rayleigh, Sec. R.S. 



On the Amplitude of Sonorous Waves which are but just Audible.^ 

 By Lord Rayleigh, Sec. Ji.S. 



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7. On the Production of Beat-tones from Two Vibrating Bodies whose 

 Frequencies are so High as to be separately Inaudible. By Alfred M. 

 Mayer. 



In the first attempts to obtain such tones use was made of steel rods of 

 rectangular section, the lengths of whose sides are to one another as 4 : 5. These 

 rods were chamfered on one edge in the length of the rods, so that by striking. 

 a rod on this edge both component tones of the rod were obtained simultaneously 

 with the resultant tone, the latter being the lower second octave of the graver 

 tone of the rod. It was impossible to obtain beat-tones by this method by reason 

 of the short duration of the resultant when the frequencies of the two component 

 vibrations of the rod surpass the limit of audibility. 



Several bird-call whistles were made in order to obtain the proper proportions 

 to give frequencies surpassing the limit of audibility and j'et to give no hissing 

 sounds. 



The most efi'ective whistle has a diameter of air-disc of 5 mm., and the holes 

 in the opposed plates of the disc are 1'2 mm. in diameter. The distance of the 

 discs of the whistles is varied and adjusted by a micrometer-screw. 



With these whistles beat-tones have been obtained when the vibrations from 

 either whistle alone were inaudible. 



Beat-tones have also been obtained by Dr. Koenig and myself in Paris with 

 tuning-forks whose frequencies surpass the limit of audibility. 



Dr. Koenig anticipated me in the production of these beat-tones by several 

 months, and has actually used those beat-tones in tuning-forks whose frequencies 

 surpass the limit of hearing. 



8. On the Variation of the Modidus of Elasticity with Change of Tempera- 

 ture as determined by the Transverse Vibration of Bars at Various 

 Temperatures. By Alfred M. Mayer. 



Lord Eayleigh in his ' Theory of Sound ' discusses the transverse vibration of 

 a bar free at both ends and supported under its two nodes, showing that we can 

 compute the frequency of the bar if we know the velocity of sound in the length 

 of the bar and the dimensions of the bar. The expression of these relations 



reduces to N l"0i!79 V -,, in which t and I are the thickness and lenffth of 



^i' o 



the bar. 



To see how closely the formula gave the transverse frequency of bars, I had 

 rods of 1-5 m. in length, 2 cm. in width, and A cm. in thickness, and of uniform 

 section, made of cast steel, aluminium, brass, glass, and white pine. These rods 

 were vibrated longitudinally at 20° C. and their frequencies determined by 

 Koenig's tonometer, whence we obtained V. Out of each rod were cut three bars, 

 each about 20 cm. long, and these bars, also at 20° C, were vibrated trans- 

 versely. The mean departure of the computed from the observed numbers of 

 transverse vibrations was ^J^, the computed frequency being always in excess of 

 the observed except in the case of glass, where the computed was below the 

 observed frequency. 



The close concordance between theory and observation shows that by vibrating^ 



• Published in the PHI. Mag., xxxviii. pp. 295-301, September 1894. 



* Jhid., xxxviii. pp. 365-370, October 1894. 



