In a traveling electromagnetic wave, the electric field is represented mathemati

Question

In a traveling electromagnetic wave, the electric field is represented mathematically as

where E0 is the maximum field strength.

In a traveling electromagnetic wave, the electric field is represented mathematically as E = E0 sin[(1.80 Times 1010 s?1)t ? (60 m?1)x] where E0 is the maximum field strength. What is the frequency of the wave? This wave and the wave that results from its reflection can form a standing wave, in a way similar to that in which standing waves can arise on a string. What is the separation between adjacent nodes in the standing wave?

Explanation / Answer

1) the general representation of electric field is

E=E0sin(?t+?x) where ?= angular frequency=2*3.14*f

on comparing both the equations we have ?=1.80*10^10 and ?=60

2*3.14*f= 1.80*10^10

=>f=2.864*10^9

2) the separation between two nodes in the standing wave is ?/2=2*3.14/2*60

=0.052m

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