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

Question

In a traveling electromagnetic wave, the electric field is represented mathematically as
E = E0 sin[(8.40 109 s^-1)t - (28 m^-1)x]
where E0 is the maximum field strength.
(a) What is the frequency of the wave?
(b)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?

I have a good idea on how to do it, but can't find representations for each variable in a formula. Any help would be appreciated.

Explanation / Answer

Data: E = E0 sin[(8.40 109 s^-1)t - (28 m^-1)x]
Solution: Gen equation: E = Eo sin [ t - k x ] (a) By comparing thje given equation with the general equation, = 8.4 x 10^9 s^-1 2 f = 8.4 x 10^9 f = 1.34 x 10^9 Hz Ans: Frequency, f = 1.34 x 10^9 Hz (b) By comparing thje given equation with the general equation, By comparing thje given equation with the general equation, k = 28 m^-1 2 / = 28 = 2 / 28    = 0.224 m Wavelength, = 0.224 m Distance between adjacent nodes, d = / 2                                                         = 0.224 /2                                                         = 0.112 m Ans: Distance between adjacent nodes, d = 0.112 m

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