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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?
(a) k
(b) ω
(c) k/ω
(d) kω

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Solution

(c) k/ω

The given quantities can be expressed as:
k is given by
k=2πλ
ω is given by
ω=2πνc=νλω=2πcλ
k/ω is given by
kω=2π/λ2πc/λ=1c

kω is given by

k×ω=2πλ×2πcλ=4π2cλ2
Thus, ​k/ω is independent of the wavelength.

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