In a traveling electromagnetic wave, the electric field isrepresented mathematic

Question

In a traveling electromagnetic wave, the electric field isrepresented mathematically as E = E0sin[(2.2 x 1010 s-1)t - (6.3 x101 m-1)x] whereE0 is the maximum field strength.(a) What is the frequency of the wave?(b) This wave and the wave that results from itsreflection can form a standing wave, in a way similar to that inwhich standing waves can arise on a string (see Section 17.5). Whatis the separation between adjacent nodes in the standing wave?

(a)

Number

Units

(b)

Number

Units

Chapter 24, Problem 49

Explanation / Answer

Given that                 E = E0 sin[(2.2 x 1010s-1)t - (6.3 x 101m-1)x] Comparing the above with the equation                                   E=E0sin[(2f)t -x/] From the above equation we get                2f =  2.2 x 1010 s-1 And         1/ = 6.3 x 101 m-1            or   = 0.0158m a) The frequency of the wave is (f) =  2.2 x1010 s-1 /2                                                 = 0.3503*1010Hz                                                 = 3.5*109Hz b) The separation between the adjacent nodes is given by                      dNN =v/2f Speed of the light (v) =3*108m/s                       dNN =  3*108m/s/2(3.5*109Hz)                                = 0.42857*10-1                                = 0.042857units                                = 0.042857units

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