﻿366 Lord Rayleigh on the Amplitude 



of the whistle experimented on, of frequency 2730, the 

 superior limit so arrived at for a sound just easily audible 

 was 8*1 x 10" 8 cm. The maximum particle velocity v and 

 the maximum condensation s are the quantities more im- 

 mediately determined by the observations, and they are 

 related by the well-known equation v = as, in which a denotes 

 the velocity of propagation. In the experiment above re- 

 ferred to the superior limit for v was '0014 cm. per second, 

 and that for 5 was 4*1 x 10 -8 . I estimated that on a still 

 night an amplitude, or velocity, one tenth of the above would 

 probably be pudible. A very similar number has been arrived 

 at by Wien *, who used an entirely different methodf. 



In co^neiion with calculations respecting the sensitiveness 

 of telephones, I was desirous of checking the abo ve estimates, 

 and made some attempts to do so by the former method. In 

 order to avoid possible complications of atmospheric refraction 

 which may occur when large distances are in question, I 

 sorght to construct pipes which should generate sound of 

 given pitch upon a much smaller scale, but with the usual 

 ecor omy of wind. In this I did not succeed, and it seems as 

 if there is some obstacle to the desired reduction of scale. 



The experiments here to be recorded were conducted with 

 tuning-forks. A fork of known dimensions, vibrating with 

 a known amplitude, may be regarded as a store of energy of 

 which the amount may readily be calculated. This energy 

 is gradually consumed by internal friction and by generation 

 of sound. When a resonator is employed the latter element 

 is the more important, and in some cases we may regard the 

 dying down of the amplitude as sufficiently accounted for by 

 the emission of sound. Adopting this view for the present, 

 we may deduce the rate of emission of sonorous energy from 

 the observed amplitude of the fork at the moment in ques- 

 tion and from the rate at which the amplitude decreases. 

 Thus if the law of decrease be e~* u for the amplitude of the 

 fork, or e~ kt for the energy, and if E be the total energy at 

 time t, the rate at which energy is emitted at that time is 

 —dE/dt, or £E. The value of k is deducible from observa- 

 tions of the rate of decay, e. g. of the time during which the 

 amplitude is halved. With these arrangements there is no 



* Wied. Ann. xxxvi. p. 834 



f The first estimate of the amplitude of but just audible sounds, with 

 which I have only recently become acquainted, is that of Toepler and 

 Boltzmann (Pogg. Ann. cxli. p. 321 (1870)). It depends upon an in- 

 genious application of v. Helmholtz's theory of the open organ-pipe to 

 data relating to the maximum condensation within the pipe as obtained 

 by the authors experimentally. The value of s was found to be 6o X 10-8 

 for a pitch of 181. — August 21. 



