Mr. R. H. M. Bosanquet on the Theory of Sound. 345 



work si 



<£)'■ 



air of amplitude A, so that the work supplied to each stream 

 per second is 



2 x i-4n 



as before. 



Cor. — Since the maximum velocity in the vibration is 



2— — =V say, we may write the energy per second, 



2prf(j±y=ipvVK 



Here pv is the mass of air which the sound traverses in a second. 



Hence the energy transmitted in a given time is the same 

 that the whole mass of air traversed would have if moving 

 with the maximum velocity of the vibration. 



This is in analogy with the general theorem, that the energy 

 of a body executing pendulum-vibrations is the same as if the 

 mass were arranged on the circumference of a fly-wheel whose 

 radius is the amplitude, and period that of the vibration — a re- 

 presentation of the motion which is frequently convenient. 



The maximum velocity is the velocity of the circumference 

 of such a wheel ; or v=2irAn. It is consequently indepen- 

 dent of the velocity of transmission. 



Cor. — Since the velocity of sound in a gas is subject* to the 

 equation 



»V=i-4n, 



where v, p may vary, but II is constant, we have, putting 

 p= — g — m t ne l as t expression, energy per second 



~ 2 v 



Hence, in the transmission of a vibration of given amplitude 

 and vibration-number through any gas, the energy per second 

 is inversely as the velocity of sound in the gas, or is propor- 

 tional to the square root of the density. 



This is the case of replacing air by hydrogen in a receiver 

 with a bell hung in it. So long as there is only air present, 

 the energy per second is simply proportional to the pressure ; 

 but if hydrogen be introduced, the Telocity of propagation is 

 increased, and the energy per second diminished in inverse 

 ratio. Ultimately when the air is replaced by hydrogen, the 



energy per second is ^ of its value for air. 



* If, like hydrogen, it have the same ratio of specific heats as air. 



