1440 
(13) 
(24 
@..4 is the critical value of © derived here, and 
shall be called the critical angle. As can be derived from 
(12), the normal solutions exist for @ > O. it - There are 
only imaginary solutions for © < O,, ++ which means that con- 
ditions for @ < Oi may not be considered steady. The 
physical sense behind that condition is that for @ < @ 
crit 
the 
reflected wave behind the incident wave is so fast that it prop- 
agates into the wavefront of the first one. 
In a pressure range O © 1% = 500emthe approximations 
(2), (4), and (5) for D, a, and u_ can be applied. Therefore 
Deri can be determined here by an explicit function. Combining 
(2), (4), and (5) with (13) gives 
I-( 
Con @ my (t(@a-k)7 
crt 
it(e-wi = Bet (14) 
DSc Me (+ lafa-k )¥ 
Considering the small value of a @ in that range of 
pressures, ©°~ O..¢ can be approximated by ON and it is 
found 
@° jznr 
es at 
crit he (14a) 
c} =_— 
O + =Q,.20 Fu ( ” in psi) (14d) 
12 
