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[(1.3 × 1010 s-1)t - (7.4 × 101 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 (see Section 17.5). What is the separation between adjacent nodes in the standing wave?

Can you show which equation(s) to use and all of the steps? I'm very confused with this one. Thank you for your time!

Answers are:

2.0687E9 Hz

.04246 m

Explanation / Answer

E = E0 sin[(1.3 × 1010 s-1)t - (7.4 × 101 m-1)x]

equation: E = Eo sin [ t - k x ]

(a)

By comparing thje given equation with the general equation,

= 1.3 × 1010 s-1

2 f = 1.3 × 1010 s-1

f = 2.068 x 10^9 Hz

(b)

By comparing thje given equation with the general equation,

k = 7.4 × 101 m-1

2 / = 7.4 × 101 m-1

= 2 / 28

   = 0.0849 m

Wavelength, = 0.0849 m

Distance between adjacent nodes, d = / 2

                                                        = 0.0849 /2

                                                        = 0..04246 m

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