202 WAVES IN AIR. [CHAP. vin. 



Eliminating p, p we find 



where 



166. Let us denote by s the condensation/ i.e. the value of 

 - at any point. If this be small, we have, by (1), 



_^ 



dx 



nearly ; and if as in all ordinary cases of sound the condensation, 

 and its rate of variation from point to point, be both small quan 

 tities whose squares, &c., may be neglected, the equation (4) be 

 comes 



The complete solution of this is 



f=F(x-c)+f(x + c)... .................. (7), 



which denotes two systems of waves travelling with velocity c, one 

 in the positive, the other in the negative direction of oc. Com 

 paring (5) with the ordinary expression of the laws of Boyle and 

 Charles, viz. 



jp 

 we find 



so that the velocity of propagation c depends, for the same gas, 

 only on the temperature 6. 



For a wave travelling in one direction only, say that of x posi 

 tive, we have 



