PLANE WAVES OF SOUND 163 



inversely as the square root of the density, provided the com- 

 parison be made at the same pressure. These conclusions are 

 in agreement with observation. 



The formula (8) will of course apply to any fluid medium, 

 provided the proper value of K be taken. In liquids the 

 difference between the isothermal and adiabatic elasticities 



3 may be neglected. For water at 15 C. we may put 

 K = 2-22 x 10 10 , p = l, in C.G.S. units, whence c = 1490 metres 



; per second. The number found by Colladon and Sturm (1826) 



I by direct observation, in the water of the lake of Geneva, was 



! 1435, at a temperature of about 8 C. 



Another formula for the velocity of sound may be noticed. 

 If H denote the height of a " homogeneous atmosphere," i.e. of 

 bi column of uniform density p Q whose weight would produce the 

 actual pressure p per unit area, we have p = gpoH, and the 

 Newtonian formula (10) becomes 



c = V(<7#); ..................... (14) 



cf. 43 (6). The velocity is accordingly that due to a fall from 

 rest through a height %H. It appears from 58 (1) that for 

 a given gas, and at a given place, H depends only on the 

 temperature. The corresponding adiabatic formula is 



(15) 



60. Energy of Sound- Waves. 



The kinetic energy of a system of plane waves is, per unit 

 area of the wave-fronts, 





where the integration extends over the space which was occupied 

 by the disturbed air in the equilibrium state. 



The work done by unit mass in expanding through a small 

 range was found in 58 to be given accurately, to the second 

 order, by the expression 



where the suffix refers to the final state. If we form the sum 

 of the corresponding quantities for all the mass-elements of the 

 system, the first term disappears whenever the conditions are 

 such that the total change of volume is zero. Again, in the 



112 



