Question

What is the simplest relationship between the angular wavenumber k and just one of the other kinematic variables?

Answer 1

Answer : $k=\dfrac{\omega}{k}$

Explanation :

The word kinematics means the study of motion. Kinematic variables gives the description of the motion of the body.

Displacement, Velocity, acceleration and time are associated with the motion of particle.

Wavenumber is defined as the frequency of wave, which is measured in cycles per unit distance.

Wave number is also defines as:

$k=\dfrac{2\pi}{\lambda}$

where, $\lambda$ is wavelength

$k=\dfrac{2\pi}{\lambda}\times \dfrac{T}{T}$

since, $\dfrac{2\pi}{T}=\omega \ and\ \dfrac{1}{V}=\dfrac{T}{\lambda}$

So, $k=\dfrac{\omega}{V}$

Where, $\omega$ is angular frequency and $V$ is velocity of wave.

Hence, the  relationship between the angular wavenumber k and and kinamatic variable V is

$k=\dfrac{\omega}{V}$