460 F. W. Boggs and N. Tokita 
The compliances of the surface will be given respectively by 
+00 
iB - iQx 
Yee Sn = ae SiGe) e dx (4.10) 
1B ' - idx 
Woe = el eae) 7e dx, (4.11) 
The Fourier transforms in this case are carried out from minus infinity to plus infinity in the 
complex plane. It is convenient to use a real notation, in which case the integrals will go 
from zero to infinity. It is worth noting, however, that the normal displacement will be an 
even function of x, whereas the tangential displacement will be an odd function of x. Asa 
consequence only the cosine transformation from zero to infinity will be important in the 
first instance, and the sine transform will be important in the second instance. 
This gives us for the surface compliance 
i 2i6 E 
7 cee). = ae F E(x) cos ax dx (4.12) 
val Gy) ———— 218 | E(x) sin ax dx, (4.13) 
V 27 F , 
Let us now suppose that the vertical vibration imparted by the knife edge gives rise to 
propagating waves having the propagating constant I. The compliances which apply to the 
normal and tangential components will be respectively given by 
_ 218 if (8) Ss il'x 
Y,2(%,) F 
oF e cos ax dx (4.14) 
V 477 
0 
me 2i8 6 (A) = Aine 
Y,,(4, 8) 
- ——_—__—_ e sin ax dx (4.15) 
J 27 F 
where f,(8) and g,(8) are functions of the frequency. 
Carrying out the integral we obtain 
