162 DYNAMICAL THEORY OF SOUND 



in absolute centimetre-gramme-second units, whence c = 280 

 metres per second. This is considerably less than the observed 

 velocity. 



The discrepancy was first fully accounted for by Laplace 

 and Poisson*. When a gas is rarefied or condensed the 

 temperature tends to fall or rise, except in so far as the 

 process is mitigated by the supply or abstraction of heat. In 

 ordinary sound-waves the condensation s changes sign so fre- 

 quently, and the temperature consequently rises and falls so 

 rapidly, that there is no time for sensible transfer of heat 

 between adjacent portions of the gas. The flow of heat has 

 hardly set in from one element to another before its direction is 

 reversed, and the conditions are therefore practically adiabatic. 

 The formula 



becomes, for small values of $, 



p=p Q (I+ys), ..................... (12) 



whence K = yp 0) as in 58, and 



c = V(7po/Po) ...................... (13) 



Putting 7=1*41 we find that the Newtonian velocity of sound 

 in air must be increased in the ratio 1'187, whence c = 332 

 metres per second at 0C. This is in good agreement with 

 direct observation. 



As there is now no question as to the soundness of this 

 explanation, and as the direct determination of 7 is a matter 

 of considerable difficulty, the formula (13) is often used in the 

 inverse manner, as a means of deducing the value of 7 for 

 various gases from the observed velocities of sound-waves in 

 them. For example, it was in this way that in 1895 the value 

 of 7 for the newly discovered gas argon was found by Lord 

 Rayleigh to lie between 1'6 and 1-7. The experimental method 

 (due to Kundt) is referred to in 62 below. 



Since p /p = R6 , the velocity of sound as given by (13) is 

 independent of the actual density, but will vary as the square 

 root of the absolute temperature. Also, so far as 7 has the 

 same value, the velocity of sound in different gases will vary 



* About, or before, the year 1807. 



