therefore, (10.3) becomes 



2 2 2 

 a - b = c tan i cot r. 



(10.4) 



If there Is no slipping between the media, then the 

 algebraic sum of the amplitudes of the incident wave and the 

 reflected wave equals the amplitude of the refracted wave, or 



a + b * c (10.5) 



Substituting (10.5) in (10.4), it is seen that 



a - b = c tan i cot r, 



(10.6) 



so that 



b = - a 



sin 

 sin 



fH^ = - 



a 



M 



1/2 



£1 

 P 



1 



T72 



cos i 

 cos r 



cos i 

 cos r 



and 



(10.7) 



_ 2a cos i sin r _ 

 sin(i + r) 



f) 



, \ 1/2 



2a cos i 



(10.8) 



cos r + cos i 



Suppose a sound wave impinges normally on a cloud in which 

 the density of the air at the same pressure is 1% less, (a possible 

 ratio owing to differences in temperature and humidity), the 

 energies in the incident, reflected and refracted waves will be 

 to each other as the ratios 



vpa^:vpb^:v'p'c^ = 160,000:1:159,999- (10.9) 



If therefore, the angle of incidence is made larger and gradually 

 approaches 90", then the reflection becomes greater, but is still 

 small for any angle up to 90°, 



33 



