﻿368 Lord Rayleigh on the Amplitude 



in the trees or the twittering of birds embarrasses the ob- 

 server, and interferes more or less with the accuracy of 

 results. 



The equality of emission of sound in various horizontal 

 directions was tested, but no difference could be found. The 

 sound issues almost entirely from the resonator, and this may 

 be expected to act as a simple source. 



When the time of audibility is regarded as known, it is 

 easy to deduce the amplitude of the vibration of the fork at 

 the moment when the sound ceases to impress the observer. 

 From this the rate of emission of sonorous energy and the 

 amplitude of the aerial vibration as it reaches the observer are 

 to be calculated. 



The first step in the calculation is the expression of the 

 total energy of the fork as a function of the amplitude of 

 vibration measured at the extremity of one of the prongs. 

 This problem is considered in § 164 of my ' Theory of 

 Sound.' If I be the length, p the density, and &> the sectional 

 area of a rod damped at one end and free at the other, the 

 kinetic energy T is connected with the displacement t) at the 

 free end by the equation (10) 



T=lplco(dr)/dt) 2 . 



At the moment of passage through the position of equilibrium 

 •>7 = and drj/dt has its maximum value, the whole energy 

 being then kinetic. The maximum value of drj/dt is connected 

 with the maximum value of rj by the equation 



(dr)/dt) max . = 2tt/t . 0) max . ; 



so that if we now denote the double amplitude by 2t?, the 

 whole energy of the vibrating bar is 



or for the two bars composing the fork 



V=ip<oW/T\{2 n y, (A) 



where pcol is the mass of each prong. 



The application of (A) to the 256-fork, vibrating with a 

 double amplitude of 20 micrometer-divisions, is as follows. 

 We have 



Z=14'0 cm., a) = *6 x 1*1 = '66 sq. cm., 



1/t=256, p = 7'8, 277=-050cm.; 

 and thus 



E = 4'06xl0 3 ergs. 



This is the w T hole energy of the fork when the actual double 

 amplitude at the ends of the prongs is '050 centim. 



