1499 
The constant of integration in equation (35) has 
been set equal to zero since it does not represent any progressive 
wave solutions. 
Eauations (33) and (35) provide two relations among 
the four functions fi, fo, and & Thus two of these functions 
2° 
may be arbitrarily assigned and the remaining two expressed in 
terms of them. To realize the condition of plane wave reflection 
under discussion, we set Be = O and let ish represent the incident 
pulse given by 
fe = 4(Gt-g% yoy? (36) 
The reflected and transmitted waves are then obtained by 
simultaneous solution of equations (33) and (35): 
(Cte) ae = ee, 37 
frlGt-t* 44) ada (37) 
iz Gt -p* Ag) Boas 7 (38) 
ra 
eae 
kk 
where Wie = COS 8, Bie 
= & cos 8 oy 
Jeter a 
These are the familiar results of conventional 
acoustic reflection theory and have been developed principally 
in order to illustrate the nature of the present mathematical 
treatment. 
eb eave 
