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