I apologize for any confusion in my previous response. Let me clarify the concept of angular wavenumber.
The angular wavenumber, often denoted as k, is a quantity used in wave propagation analysis to describe the spatial variation of a wave. It is defined as the rate of change of the phase of the wave with respect to distance. The correct relationship between the angular wavenumber and the wavelength is given by:
k = 2π / λ
where λ represents the wavelength of the wave. This formula establishes that the angular wavenumber is equal to 2π divided by the wavelength.
The expression you mentioned, k(Pi) = 2π, is incorrect. The value of k depends on the specific wavelength under consideration and is not equal to a constant value like 2π. Instead, it is proportional to the reciprocal of the wavelength, indicating that shorter wavelengths correspond to larger values of the angular wavenumber.
To summarize, the correct relationship between the angular wavenumber (k) and the wavelength (λ) is given by k = 2π / λ.