So, it immediately follows that As a result, we observe an inverse relation between the angular frequency and wavevector.
If the wave has higher frequency oscillations, the wavelength must be shortened for the phase velocity to remain constant.
[2] Additionally, the phase velocity of electromagnetic radiation may – under certain circumstances (for example anomalous dispersion) – exceed the speed of light in vacuum, but this does not indicate any superluminal information or energy transfer.
[citation needed] It was theoretically described by physicists such as Arnold Sommerfeld and Léon Brillouin.
For this it is necessary to mathematically write the beat or signal as a low frequency envelope multiplying a carrier.
This commonly appears in wireless communication when modulation (a change in amplitude and/or phase) is employed to send data.
To gain some intuition for this definition, we consider a superposition of (cosine) waves f(x, t) with their respective angular frequencies and wavevectors.