WAVEGUIDE TRANSMISSION 



331 



metrical relations shown in the lower part of Fig. 6.4-2. Phenomena 

 similar to this are sometimes observed when water waves, coming in from 

 the ocean, break upon the beach. If the approach is nearly perpendicular, 

 the point at which the wave breaks may proceed along the beach at a 

 phenomenal speed. A similar effect may be produced by holding at arm's 

 length a pair of scissors and observing the point of intersection as the blades 

 are showly closed. A relatively slow motion of the blades leads to a rather 

 rapid motion of the point of intersection. 



Since, in the case of incident waves, the apparent velocity is Vz = z'/sin 6, 

 the corresponding wavelength is A^ — X/sin d. Both quantities play an 

 important part in the picture of waveguide transmission to be drawn later. 

 In particular, the apparent velocity v^ will prove to be identical with a 

 quantity known as phase velocity. 



Path of Incident 

 Line of Force 



/ 



h:=h,;+h„:.2h„ 

 h[= h^- h^= 



e''= E - e' = 



Electric Vector-^ 



Electric Vector 



Path of Reflected 

 Line of Force 



(directed away (directed toward 



from observer) observer) 



Fig. 6.4-3. Relationship Ijetween various components of E and H before and after reflection 



by a metal plate. 



A second observer located at the interface, shown in Fig. 6.4-2, endowed 

 with better vision and able to single out particular lines of force may obtain 

 a somewhat different view of reflection. If he observes a particular line of 

 force such as (4) in Fig. 6.4-2 for the considerable period of time, /, required 

 for it to approach the conducting interface [Figs, (a) to (c)] and recede to 

 a comparable distance [Figs, (c) to (e)], he will note that, whereas the line 

 of force has really traveled a total distance vl, its effective progress parallel 

 to the interface has been v'l = vi sin Q. (See geometrical relations in lower 

 part of Fig. 6.4-2.) This provides another kind of velocity {v' = v sin 0) 

 known as group velocity. It is the effective velocity with which energy is 

 propagated parallel to the metal surface. It approaches zero at perpen- 

 dicular incidence. It will be observed that 



V = Vz sm" 



