﻿of just audible Aerial Waves. 369 



As has already been shown, the energy lost per second is 

 &E, if the amplitude vary as e~* kt . For the present purpose 

 k must be regarded as made up of two parts, one k x repre- 

 senting the dissipation which occurs in the absence of 

 the resonator, the other k 2 due to the resonator. It is the 

 latter part only which is effective towards the production of 

 sound. For when the resonator is out of use the fork is 

 practically silent ; and, indeed, even if it were worth while 

 to make a correction on account of the residual sound, its 

 phase would only accidentally agree with that of the sound 

 issuing from the resonator. 



The values of ki and k are conveniently derived from the 

 times, ti and t, during which the amplitude falls to one half. 

 Thus 



k=2 log e 2 . It, & 1= 2 lo ge 2 ./*! ; 

 so that 



& 2 =21og e 2 . (1/f-lAO =1-386 (1/t-l/ti). 



And the energy converted into sound per second is & 2 E. 



We may now apply these formulas to the case, already 

 quoted, of the 256-fork, for which £ = 9, ^=16. Thus t 2 , the 

 time which would be occupied in halving the amplitude were 

 the dissipation due entirely to the resonator, is 20*6 ; and 

 k 2 = '06 74. Accordingly, 



& 2 E = 267 ergs per second, 

 corresponding to a double amplitude represented by 20 

 micrometer-divisions. In the experiment quoted the duration 

 of audibility was 12 seconds, during which the amplitude would 

 fall in the ratio 2 12 / 9 : 1, and the energy in the ratio 4 12/9 : 1. 

 Hence at the moment when the sound was just becoming 

 inaudible the energy emitted as sound was 42*1 ergs per 

 second*. 



The question now remains, What is the corresponding 

 amplitude or condensation in the progressive aerial waves at 

 27*4 metres from the source ? If we suppose, as in my former 



* It is of interest to compare with the energy-emission of a source of 

 light. An incandescent electric-lamp of 200 candles absorbs about a 

 horse-power, or say 10 10 ergs per second. Of the total radiation only 

 about -^ part acts effectively upon the eye ; so that radiation of suitable 

 quality consuming 5 X 10 5 ergs per second corresponds to a candle-power. 

 This is about 10 l times that emitted as sound by the fork in the experi- 

 ment described above. At a distance of 10 2 X 30, or 3000 metres the 

 stream of energy from the ideal candle would be about equal to the 

 stream of energy just audible to the ear. It appears that the streams of 

 energy required to influence the eye and the ear are of the same order 

 of magnitude, a conclusion already drawn by Toepler and Boltzmann. 

 — August 21. 



Phil. Mag. S. 5. Vol. 38. No. 233. Oct. 1*94. 2 C 



