When studying the velocity of waves, or how fast waves are moving, there are two distinct types that can be calculated, which are phase velocity and group velocity. Phase velocity measures the velocity of a single wave, while group velocity measures the velocity of a wave packet, or envelope. A wave packet is a group of waves that move as a single unit, and so can be measured as a single entity.
Velocity is calculated by measuring the distance moved during a particular time. Measuring phase velocity involves measuring the distance one wavelength moves in a period of time. A wavelength is the distance from the crest, or top, of one wave to the crest of the next wave. Phase velocities and group velocities do not have to be the same in a wave packet.
Several different relationships can be observed between phase and group velocities. When the phase and group velocities are the same, each component wave moves with the entire packet, or the waveform moves as a single unit. If the phase velocity is equal to the negative group velocity, then the component waves are moving in the opposite direction to the wave packet.
The phase and group velocities can also be greater than or less than each other. Waves with phase velocities greater than the group velocity will be moving quicker than the envelope. The opposite is true when the group velocity is greater. In this case, the component waves are moving slower than the complete envelope.
In addition to the above scenarios, either the phase velocity or the group velocity can equal zero. When this happens, either the component waves or the wave packet is stationary. With a phase velocity of zero, the wave packet moves over stationary component waves. A group velocity of zero means that the envelope is still and the component waves are moving through it.
The phase velocity will differ for different types of media. This is because the properties of the medium play a role, so light waves, sound waves and waves in different liquids can react differently. Also, the frequency of the waves can have a direct effect on the phase velocity, as different frequencies of waves are usually traveling at different speeds. The phase velocity of waves can also be measured within a vacuum. This has to be taken into consideration as the permeability and permittivity of the vacuum will have a direct effect on the phase and group velocities of the medium being measured.