The relationship between angular frequency (ω) and wavelength (λ) in an electromagnetic wave is given by the wave equation:
c = λω,
where c represents the speed of light in the medium through which the wave is propagating.
In this equation, λ is the wavelength of the wave, which is the distance between two consecutive crests or troughs of the wave. It is typically measured in meters (m).
ω is the angular frequency of the wave, which is the rate at which the wave oscillates in radians per unit time. It is related to the ordinary frequency (f) of the wave by the equation:
ω = 2πf,
where f is the frequency of the wave measured in hertz (Hz).
Therefore, the relationship between angular frequency and wavelength can be expressed as:
c = λ(2πf),
or
c = λω.
From this equation, it is evident that as the angular frequency increases, the wavelength decreases, and vice versa, while the speed of light remains constant. In other words, higher-frequency waves have shorter wavelengths, and lower-frequency waves have longer wavelengths.