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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
Solution
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.
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