1479 
y is always negative, Gz was set equal to fel or to make the 
real exponential term of eq. (3) tend to zero as y—» —o%O , 
For the same reason one must then use / W ]} rather than & in 
the same term. 
The boundary conditions to be satisfied are: 
an ae (4) 
WANG Pap ie ed, 
(2G Seana 
al y= ‘e) 
(5) 
2.2 Application of these boundary conditions leads to the 
following expressions for the incident and transmitted waves: 
Pe reespiec(e- aie 97) ) <2 (oi aaa 
P 2P. Cos € exp)ewo(t-a,x) ¢ [2/6 fw + al | (7) 
It will be seen that the factor /w/ |v enters through 
the differentiations with respect to y in equation (5). This 
factor is simply set equal to unity in Rayleigh's treatment! ana 
in Navord 424 since in the consideration of harmonic wave trains 
negative values of W have no physical significance. 
In the present treatment, however, we wish to apply the 
phase shift of equation (6) to the Fourier spectrum of an 
exponential transient and to do this by utilizing the general 
-~j3- 
