1496 
4. Alternative treatment of plane wave reflection as a boundary 
value problem. 
4.1 It will be noted in the harmonic wave solutions (eauations 
(6) ana (7)) that 7 and xX always appear in the combination 
( &—e,X ) where &, = Cas Sin @, . Thus the wave pattern as 
a whole moves in the direction of increasing x with a 
velocity G/s/n®6, . 
Since we are interested in pulses rather than in 
harmonic wave trains, we are led to investigate the conditions 
under which a more general pressure field may be propagated 
with constant velocity parallel to the surface of discontinuity. 
Such a pressure field may be written in the form: 
Pi tPr 22 4(y, 6,0 - -x) 2 fF (Gy) 
gi ies SHED Ct fa) = Gy: %) (25) 
where “ue Ot-fx 
The pressure fields in regions 1 and 2 must satisfy 
the wave equations: 
(Sy Bat 
ns 2 (26) 
V ‘pz = Lh O a 
Cae 
= 20 = 
