Wave Number (k) 2pi/lambda = Radians /Unit Distance ?

[Point Conception]

The wave number k = 2π/λ . But is defined as radians per unit distance. What is the correlation here between the
wavelength and radians ?

 

[Chandra Prayaga]

It is not a correlation. It is a definition. The quantity 2π/λ, which occurs in the mathematical description of wave motion, is called the wave number k. If you write a wave function as sin (kx - ωt), the argument of the sine function should be in radians. So k multiplied by x must be in radians. Since x is a distance, k has units of radians per unit distance.