The LaTeX: yy-component of the electric field of an electromagnetic wave traveling in the LaTeX: + x + x-direction through vacuum obeys the equation LaTeX: E_y = (375/; {/rm N/C}) / cos[kx - (2.20/!/times/!10^{14}/; {/rm rad/s}) t]E y = (375 N / C) cos ⁡ [ k x - (2.20 * 10 14 r a d / s) t ]. What is the wavelength of this electromagnetic wave in micrometers?

Given that,

Wave equation is

Ey = 375•Cos (kx - 2.2 * 10¹⁴t)

Generally,

The wave equation is written as

Ey = Eo•Cos (kx-wt)

Where

K is wave number

ω is the angular frequency

So, comparing this to the the given wave equation, we found out that,

ω = 2.2 * 10¹⁴ rad / s

Then,

ω = 2πf

f = ω / 2π

From the relationship between wavelength and speed

v = fλ

Substitute for f

v = λ * ω / 2π

In electromagnetic we are dealing with speed of light, then, v = c

c = λ * ω / 2π

c is speed of light in vacuum and it's value is

c = 3 * 10^8 m/s

Make wavelength subject of the formula

λ = 2π * c / ω

λ = 2π * 3 * 10^8 / 2.2 * 10¹⁴

λ = 8.57 * 10^-6 m

λ = 8.57 μm

The wave length is 8.57 μm