TJic Propagation of Sound. 



On Sound propagated through an atmosphere, in which 

 the surfaces of constant density are parallel planes, 

 in a direction perpendicular to these planes. By 

 Ralph Holmes, B.A. 



{Received May 8th, i88p.) 



We will endeavour to obtain a solution of this question 

 when the law of change of density is any whatsoever, pro- 

 vided this change is very small. 



With the usual notation let /, p be equilibrium density 

 and pressure at any point x, p +p' ; p + p' what these become 

 when there is wave motion. 



Then 



^_ ^ = X 

 p dx ^ 



I d . {p+p') _^ _dn _ du 



p + p' dt dt dx 



Hence to first order of/', p', u, we have 



\ dp^ _p d_l ^ _du^ /jx 



P dx p2 dx dt ^'' 



Also from the equation of continuity, 



^M-J^^ = (ii.) 



dt dx ^ ^ 



Now, whenever we have compression or rarefaction of 

 air due to a wave of sound, on the supposition that there is 

 no ingress or egress of heat, we have the relation that the 

 change of pressure is y times as great as it would have been 

 had there been no change of temperature. Thus 

 I ^•p+p''_ y c.p + p'' 

 p+p' c . t p + p' ^ . t- 

 But 



^ d d 

 — = T- + ^(-1-- 

 ht dt dx 



