Question

An electromagnetic wave going through vacuum is described by
E = E₀ sin (kx − ωt).
Which of the following is/are independent of the wavelength?

Options

• k

• ω

• k/ω

• kω

Answer 1

k/ω

The given quantities can be expressed as :
k is given by

`k = (2pi)/λ`

ω is given by 

`ω = 2piv`

`c = vλ`

⇒ `ω = 2pic/λ`

k/ω is given by 

`k/ω = (2pi"/"λ)/(2pic"/"λ) = 1/c`

kω is given by 

`k xx ω = (2pi)/λ xx (2pic)/λ = (4pi^2c)/λ^2`

Thus, ​k/ω is independent of the wavelength.