STUDIES IN RADIO BROADCAST TRANSMISSION 163 



If we assume the distances to be measured in any desired units 

 and call them di and d^ our equation will still hold provided we divide 

 each distance by the wave length measured in the same units, thus 



-^— — ^ = a whole number = :v:; 



A 



rearranging this and writing -^ for X where V equals the velocity of 



r 



the waves, we have 



If now we assume {di'-di!) to be fixed we find that Fcan have a 



series of values which are integral multiples of —-, — j-, which we 



Oi — di 



may call the frequency spacing interval. That is, with changing 

 frequency E will go through maximum values with frequency at a 

 series of frequencies beginning theoretically with zero and extending 

 upward in regular spacing to infinity. 



The spacing interval is obviously that number of cycles which cor- 

 responds to the lowest finite frequency in the series, namely, the 

 frequency for which the distance (di'—di) is just one wave length 

 since when x = unity equation (4) becomes 



V . . , 



Fi = -77 — y-, = the spacmg mterval. (5) 



di — tt2 



By using the same process on equation (3) we find that E has 

 minimum or zero values at another series of frequencies having the 

 same spacing interval but lying midway between the frequencies at 

 which maxima occur. 



Thus it is apparent that with fixed path length difference the 

 amplitude of the field E will be different for different frequencies, 

 ranging from maxima of (^1 + 62) down to minima of zero if the polar- 

 ization planes and amplitudes of the two vertical components are 

 equal. 



Furthermore, still thinking of equation (1) as representing two 

 vectors, it is evident that the phase of the resultant field is different 

 for different frequencies even though these different frequencies 

 had exactly the same starting phase at the source. 



If the paths are changing with time, the field at a given point, as 

 has already been pointed out, will go through time fluctuations. 

 Another way to look at this is that there is a space pattern of maxima 



