Physical Significance/Interpretation of Angular Wave Number.

ApuroopS

My doubt is on the angular wave number 'k'

in case of a sinusodal wave on a string,
the angular wave number

k = (2*pi)/lambda

lambda being the wave length of the wave.
What does 'k' signify in physical terms ?

for e.g.

general wave number = 1/lambda

again, lambda being the wavelength of the wave.

the physical significance for this is basically the number of wavelengths per unit distance


so along those lines, does the angular wave number stand for number of wavelengths per radian ??
Or something else ?

any help in clarifying this will be appreciated.
Cheers.

btw, my apologies in advance for the bad presentation, but can't actually texify from my cellphone.