the Propagation of Sound. 451 



the molecules of hydrogen are moving- four times as fast as 

 the molecules of oxygen ; and on this account the wave is 

 propagated four times as fast, not because the propagating 

 molecule is heavy or light. 



16. Case of Heated Rarefied Air. — When air unconfined 

 and free to expand is heated, the velocity of sound is found to 

 be increased. This, according to the old theory, is considered 

 to be due to the diminished density of the air, or the diminished 

 number of molecules attendant on the expansion of the air. 

 Now 3 in accordance with the kinetic theory, this increased velo- 

 city of propagation of the wave is simply explained by the in- 

 creased velocity of the air-molecules which propagate it, atten- 

 dant on the application of heat to the air, the motion of the 

 molecules representing the " heat " and their velocity being a 

 measure of the " temperature." The increase in the velocity 

 of the molecules of air attendant on the application of heat 

 pushes the surrounding air back, and causes the heated portion 

 to be rarefied, thus diminishing its density. The density of 

 the heated portion may therefore be taken as a convenient 

 measure of the velocity of its component molecules, upon which 

 the velocity of propagation of the sound-wave depends. Thus 

 it may be a convenient rule that the velocity of sound in 

 heated rarefied air is inversely proportional to the square root of 

 the density of the air, the cause of this being that the molecu- 

 lar velocity is itself inversely proportional to the square root of 

 the density (i. e. in air free to expand and change its den- 

 sity). The diminished density of the heated rarefied air can- 

 not, however, be said to be the cause of the increased velocity 

 of the sound-wave ; the diminished density is rather the effect 

 of the increased molecular velocity, which itself is the cause 

 of the increased velocity of the wave. 



17. So the velocity of sound in different gases is found to 

 be inversely proportional to the square root of the specific 

 gravities of the gases : but this is simply due to the fact that 

 the specific gravity of a gas is as its molecular weight ; 

 and the molecular velocity, upon which the velocity of pro- 

 pagation of the sound-wave depends, is itself inversely pro- 

 portional to the square root of the molecular weight. 



18. Case of Heated Confined Air. — When air (or any gas) 

 is confined in a vessel so as to prevent expansion and then 

 heated, the velocity of sound is found to be augmented. This 

 augmentation of velocity, according to the kinetic theory, is 

 due to the same cause as in the previous case (when the air 

 was unconfined), viz. to the increased velocity of the air mole- 

 cules attendant on the application of heat. According to the 

 old theory, the augmented rate of propagation of the wave is 



2G2 



