The wavenumber, typically denoted by the symbol "k," is defined as the spatial frequency of a wave. It represents the number of complete wavelengths (cycles) that occur per unit distance. The wavenumber is related to the wavelength (λ) of a wave through the equation:
k = 2π/λ
In this equation, 2π/λ is indeed the correct expression for the wavenumber. The factor of 2π arises due to the periodicity of the wave, as it represents one complete cycle (2π radians) divided by the wavelength (λ).
Therefore, the wavenumber is expressed as 2π divided by the wavelength (k = 2π/λ), not as 1 divided by the wavelength (k = 1/λ).