direction i.e., in the azimuthal direction in a cross sectional plane, after one complete rotation we reach to the same location. In other words, the function  is periodic in  over  . In  direction, the function is a harmonic function that is,
where  is an integer. This functional form represents a field which will repeat itself after one rotation or when  changes by multiples of  .
Substituting for the  in the wave equation the only unknown function remains to be evaluated is  .
The wave equation therefore becomes
 (9)
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direction. If a wave travels in 
direction then its z-variation should be 
. That is to say that 
variation we can use the following argument . From Figure1 we can note that, if we move only in the 
