310 BELL SYSTEM TECHNICAL JOURNAL 



air, the velocity iv is substantially 3()0,()00,()00 meters per second (186,000 

 mi per sec). For other media :' = t'a/\//Xre, • Thus it will be seen that, by re- 

 {)lacing the air normally found between the two wires of a transmission line 

 by another medium such as oil (e,. = 2 and Mr = D, the wavelength will be 

 reduced by a factor of 1 '•\/2. 



If .1.1 is the ma.ximum amplitude reached by the oscillating source during 

 any cycle, the amplitude at any time /, measured from an arbitrary begin- 

 ning, may be e.xpressed by the equation 



.•1 = Au sin (co/ + 4>) = --In sin (-'^ ?■/ + j (6.2-1) 



where 4> is the initial |)hase of the amj)Htude relative to an arbitrary refer- 

 ence angle 



If the transmission line is free from dissipation and we choose a datum 

 point in a plane at right angles to the direction of propagation and at a 

 distance far enough from the source that the lines of force have had an oppor- 

 tunity to conform to the wire arrangement and if we designate the electric 

 intensity at this point as E i and the corresponding magnetic intensity as 

 //ii, then the electric and magnetic intensities at other corresponding points 

 at a distance z further along the line may be represented by 



E = Ei) sin — (:; — vl) 



A 



and 



// = Ih sin — (c - vl) (6.2-2) 



A 



These equations are the trigonometric representations of an unattenuated 

 sinusoidal wave of electric intensity and magnetic intensity traveling in a 

 positive direction along the z axis. They are plotted in the yz and xz planes of 

 Fig. 6.2-3(b). An electromagnetic configuration similar to the above but 

 traveling in the opposite direction is given by 



E - £„ sin ^'^ {z + vl) 



A 



// = //„ sill ^"^ (:; -f- vl) (6.2 3) 



These c(|uali()iis may i)c furlluT conlirmcd by |)li)lliiig arbitrary \"alues on 

 rectangular-coordinalc pajjcr. In an infmitc line the magnetic intensity H 

 and the electric intensity E are in the same i)hase as shown in I'ig. 6.2-3. 



