1511 
b= Lf Pa. 
(Note that Jd ee imaginary if Bee. ). In addition a 
spherical attenuation proportional to 1A is to be applied to the 
amplitude of the wave. 
The first term of this expansion is the familiar 
reflection coefficient for plane waves incident at an angle O e 
The second term is frequency dependent and represents a correction 
term which will be small for high frequencies, that is provided 
fy, RE* = A fer RS is small compared to unity (A is the wave length 
corresponding to angular frequency ©). For angles not too close 
to the critical angle (which makes d=0 ), the reauirement is 
essentially that R be much greater than a wave length. 
For the geometry assumed in Figure 4, we have 
Poh pees 
Taking as a typical wave length the distance a signal would travel 
in twice the time constant: 
A 21.5 ft., 
we have 
A /a7R (617 = ear 
This confirms that the plane wave approximation is poor for the 
case of Figure 4, and in general when the angle of incidence is 
near the critical angle. 
- 35 
