38 BELL SYSTEM TECHNICAL JOURNAL 



PART III 



REFLECTION, REFRACTION, SHIELDING AND POWER 



ABSORPTION 



Special Applications 



The general formulae derived in the preceding part are directly 

 applicable to a variety of special cases such as reflection of plane 

 waves at a plane boundary, shielding action of cylindrical shields upon 

 electric waves produced by an infinite parallel pair of electric current 

 filaments, shielding action of spherical shields upon electric waves 

 produced by a coil or a condenser, etc. Of course, most of these 

 results have already been obtained and published, each special prob- 

 lem having been treated on its own merits rather than as a particular 

 case of a general formula. For this reason, we shall confine ourselves 

 largely to a discussion of those aspects of reflection which are par- 

 ticularly illuminated by the general point of view. 



Cylindrical Waves 



Consider two parallel wires carrying equal and opposite alternating 

 currents. At a distance from the wires two or three times as large 

 as their interaxial separation, the wave is substantially that of a line 

 doublet and the radial impedance in free space is approximately ^ ioiixp 

 so long as p is much less than the wave-length. This restriction on p 

 is permissible in the present communication art. In metallic media 

 this expression for the radial impedance is good only at very low fre- 

 quencies. At high frequencies the radial impedance in metallic media 

 is substantially ^ yjiosn/g. 



If the pair of wires is surrounded by a metal cylinder, the latter 

 will act as a shield by virtue of reflections taking place at the boundary 

 and attenuation through the shield. 



The attenuation constant is substantially ^irixgj nepers per meter. ^^ 

 Thus the attenuation in logarithmic units through the shield is pro- 

 portional to the first power of its thickness and to the square roots of 

 the conductivity, the permeability and the frequency. 



The reflection loss depends upon the impedance ratio. In the 

 neighborhood of / = 0, the impedance ratio is seen to be equal to the 

 ratio of the permeabilities. Consequently, at very low frequencies 

 non-magnetic shields are relatively inefficient since there is no reflec- 



* Equation (12). 



^ The approximate error is l/2o-p; at 10 kc. the error is about 2.5 per cent at a 

 distance 1 cm. from the line source. 



1" This is true even at low frequencies if the shield is thin compared to its diameter. 

 Otherwise, the cylindrical divergence of the wave must be taken into account. 



