﻿370 Amplitude of just audible Aerial Waves. 



calculations, that the ground reflects well, we are to treat the 

 waves as hemispherical. On the whole this seems to be the 

 best supposition to make, although the reflexion is doubtless 

 imperfect. The area S covered at the distance of the observer 

 is thus 2tt x 2740' 2 sq. centim., and since * 



S.ia^ 2 = S.^aV = 42-l, 

 42-1 



we 



find 



and 



7r x 2740 2 x -00125 x 34100 3 ' 

 5 = 6-0 xlO" 9 . 



The condensation s is here reckoned in atmospheres; and the 

 result shows that the ear is able to recognize the addition and 

 subtraction of densities far less than those to be found in our 

 highest vacua. 



The amplitude of aerial vibration is given by asr/'Iir, where 

 1/t = 256, and is thus equal to ] '27 x 10 -7 cm. 



It is to be observed that the numbers thus obtained are still 

 somewhat of the nature of superior limits, for they depend 

 upon the assumption that all the dissipation due to the resona- 

 tor represents production of sound. This may not be strictly 

 the case even with the moderate amplitudes here in question, 

 but the uncertainty under this head is far less than in the case 

 of resonators or organ-pipes caused to speak by wind. From 

 the nature of the calculation by which the amplitude or 

 condensation in the aerial waves is deduced, a considerable 

 loss of energy does not largely influence the final numbers. 



Similar experiments have been tried at various times with 

 forks of pitch 384 and 512. The results were not quite so 

 accordant as was at first hoped might be the case, but they 

 suffice to fix with some approximation the condensation 

 necessary for audibility. The mean results are as follows : — 



d, frequency = 256, 5 = 6*0 xlO -9 , 



g\ „ =384, 5 = 4-6xl0- 9 , 



c", „ =512, 5=4-6 xlO" 9 , 



no reliable distinction appearing between the two last numbers. 

 Even the distinction between 6'0 and 4- 6 should be accepted 

 with reserve; so that the comparison must not be taken to 

 prove rnuch more than that the condensation necessary for 

 audibility varies but slowly in the singly dashed octave. 



* < Theory of Sound/ § 245. 



