Dr. Schroder van der Kolk on the Velocity of Sound. 39 



casioned by a difference of pressure, in the one case, between the 

 wave-crest and the surrounding air, and in the other between 

 the air and the trough of the wave. And since it follows from 

 the formula that these differences are equal to each other, the 

 two cases are identical. 



Accordingly the velocity varies with the intensity. 



When sound is propagated in a tube, the intensity remains 

 nearly unchanged, and is then given by formula (2). 



If, on the contrary, the wave spreads out in space, the inten- 

 sity diminishes, and the velocity is consequently different every 

 instant. The time in w T hich the wave will traverse a given dis- 

 tance is easily found in the following manner. 



Let the radius of the sound-wave, which in this case is a 

 sphere, be R, when the amount of condensation is represented 



AV 

 by -yr- ; we have then to determine the time which must elapse 



before the wave has attained the radius r, that is to say, the 

 time! in which it traverses the distance r — R. The work done 

 in the condensation, or the energy of the wave, is = 4R 2 7rpAV, 

 if jo is the pressure measured by the barometer. 



The energy of the wave when the radius is p is = 4p 2 7rpdV ; 

 and since the energy of every wave is constant, we have 



4R 2 7rpAV=4 / 3 2 7rpdV, 



dV=~ 2 AY; 

 P 



and hence equation (2) becomes 



._ /5HJ8 .fn 7(y+i)-2 .AVR«i 



where AV is the condensation in the sound-wave R, and p 

 alone is variable. 



If, for the sake of simplicity, we put 



/?H/3 A 7(7 + 1) -2 AV ^ 2 



we get 



From the equation 



