COS -jT^ (at - X cosa + y sina) (9.2) 



respectively, and the expression for the resultant is 



s = cos =r- (at - x cosa - y sina) + cos -? (at - x cosa ■•■ y sina) 



= 2 cos ~ (at - X cos a) cos ^ (y sin a). (9.3) 



Since the expression on the right side of (9.3) is an even 

 function of y, s is symmetrical with respect to the x-axis, so 

 that there is no motion across that axis. Under these conditions, 

 a rigid wall placed along the x-axis would in no way impede the 

 motion. Therefore, the resultant ray (s) satisfies the boimdary 

 condition that there be no motion across the x-axis. 



From the expression (9.3) it is seen that the resultant wave 

 (s) on the xy plane advances parallel to the x-axis unchanged in 

 type and with a constant velocity a/cosa. 



If, of course, a = irr which is the case for normal incidence, 

 then (9.3) reduces to 



s = 2 cos (^ at) cos (^ y), (9.4) 



and we have standing waves, 



4 

 10. Reflection at an air interface 



Let two adjacent air masses, I and II be separated by the 

 boundary M. If they have the same pressure, but different densities 

 due to differences in temperature and/or humidity, then a wave pro- 

 ceeding from air mass I to air mass II will undergo a change in 



4. Humphreys, W. J. (1929): Physics of the Air . Second edition, 



L'IcGraw-Hill Book Company, Inc., New York and London, pp. 407-410. 



30 



