The electric field of an electromagnetic wave ina vacuum is ey= (20 v/m)sin((6.28x108)x -2πft), where x is in m and t is in s. what are the wave’s (a) wavelength, (b) frequency, and (c) magnetic field amplitude?

(a) 10 nm

(b) 1 Hz

(c) 20 V/m

Explanation

The equation of a progressive wave is given by:

                                y = Asin(kx ± ωt)

where;

A is the amplitude of the wave in meters

y(x,t) is the displacement in meters

k = 2π/λ is the propagation constant

ω = 2πf is the angular frequency in radian per seconds

The equation now becomes;

                                   y = Asin((2πx)/λ ± 2πft)

(a) Comparing Ey= (20 V/m)sin((6.28x10⁸)x -2πft) with the general equation

                                   (2πx)/λ = 6.28 × 10⁸

                                   λ = 2π / 6.28 × 10⁸

                                   λ = 1.0 × 10⁻⁸ m

                                   λ = 10 × 10⁻⁹ m

                                   λ = 10 nm

(b) Comparing Ey= (20 V/m)sin((6.28x10⁸)x -2πft) with the general equation

                                    2πft = 2πft    

                                         f = 1 Hz

(c) Comparing Ey= (20 V/m)sin((6.28x10⁸)x -2πft) with the general equation

                                     A = 20 V/m

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