Question

what is a wave vector?

Answer 1

@Vincent-Lyon.Fr

Answer 2

You know time period T and pulsation \(\omega\).

k is to wavelength \(\lambda\) what \(\omega\) is to time period T.
In this sense is it a space-pulsation.

Look at expression k = 2\(\pi\)/\(\lambda\)
If you ignore the numerical factor 2\(\pi\), k is the number of full wave oscillations in 1 metre of space.

1/\(\lambda\), known as wave-numer is expressed in \(m^{-1}\)
and k is expressed in rad/m.

Now, the number of waves mentioned lies in a certain direction, so to provide for all possible directions, k can be turned in a vector :

\(\vec k=2\pi/\lambda \;\vec u\) where \(\vec u\) is the unit-vector in the direction of propagation.

Answer 3

why should we multiply the factor 2pi

Answer 4

Because as it is easier to write \(\cos\omega t\) than \(\cos\Large \frac{2\pi t} {T}\),

is is easer to write \(\cos \vec k.\vec r\) than \(\cos \;(\Large \frac{2\pi} {\lambda}\normalsize \vec u . \vec r)\)

Answer 5

thanks