1500 
If we were interested in the case of a plane wave 
progressing from a medium of high to low sound velocity, we could 
See F; = 0 and express g, and f, in terms of gg. The results 
zg 
would be analagous to equations (37) and (38). 
4.4 We now consider case (2) where equation (27) is hyperbolic 
while equation (28) is elliptic. The latter equation does not 
have a progressive wave solution, and the problem is somewhat more 
complicated than in case (1). Under such circumstances, if we 
specify the pressure along the surface y ® o, then the solution 
is completely determined in the region y < o, provided that we 
require it to remain finite as y—»~-eo . This pressure field 
can be expressed in terms of the Fourier integral: 
G4. ) = en) [de a Go,v) expféus(u-v) + ply ¥]aY 40) 
where 
p*= yee Capes, (41) 
from equation (28). 
The boundary conditions (4) and (5) determine the 
pressure and normal derivative of the pressure at the surface 
of discontinuity. This completely fixes the solution in the 
hyperbolic region, where we can again write the progressive wave 
- 2h. 
