Energy and Apparent Intensity of Sounds of different Pitch. 175 

 And if we take vt— x = at the lower limit, 



p=(^)V 



And the potential work in the length v traversed by the sound 

 second = v 3 pl — -J . 



in one 



This is expressed in foot-pounds; for v 2 p is in terms of the 

 atmospheric pressure over the unit section, v is a number of 



feet, and — a number. 

 A. 



We have now to estimate the kinetic energy of each disk of 



the photographed column, 



Kinetic energy of disk dx 



= <j v*p ( -T-"~ j cos 2 ^— (vt — x) dx, 



which is identically the same expression we had before. We 

 have therefore simply to double the above result; and we get 

 for the total energy delivered in one second, 



*"(?)'• 



If we apply to this result the experimental law, that the appa- 

 rent intensity is directly as the energy and inversely as the wave- 

 length or periodic time, we have 



T , a * 



1= const, -y- 



And instead of the laws given in the writer's communication of 

 last November, we have the following : — 



The apparent intensities of sounds of different pitch are pro- 

 portional to the squares of the amplitudes, and inversely as the 

 cubes of the wave-lengths. 



In sounds of the same apparent intensity, the squares of the 

 amplitudes vary as the cubes of the wave-lengths. 



