In physics, a wave packet (also known as a wave train or wave group) is a short burst of localized wave action that travels as a unit, outlined by an envelope. A wave packet can be analyzed into, or can be synthesized from, a potentially-infinite set of component sinusoidal waves of different wavenumbers, with phases and amplitudes such that they interfere constructively only over a small region of space, and destructively elsewhere. Any signal of a limited width in time or space requires many frequency components around a center frequency within a bandwidth inversely proportional to that width; even a gaussian function is considered a wave packet because its Fourier transform is a "packet" of waves of frequencies clustered around a central frequency. Each component wave function, and hence the wave packet, are solutions of a wave equation. Depending on the wave equation, the wave packet's profile may remain constant (no dispersion) or it may change (dispersion) while propagating.
👉 Wave packet in the context of Phase velocity
The phase velocity of a wave is the speed of any wavefront, a surface of constant phase. This is the velocity at which the phase of any constant-frequency component of the wave travels. For such a spectral component, any given phase of the wave (for example, the crest) will appear to travel at the phase velocity. The phase velocity of light waves is not a physically meaningful quantity and is not related to information transfer.
Wave packet in the context of Tsunami
A tsunami (/(t)suːˈnɑːmi, (t)sʊˈ-/ (t)soo-NAH-mee, (t)suu-; from Japanese: 津波, lit. 'harbour wave', pronounced [tsɯnami]) is a series of waves in a water body caused by the displacement of a large volume of water, generally in an ocean or a large lake. Earthquakes, volcanic eruptions and underwater explosions (including detonations, landslides, glacier calvings, meteorite impacts and other disturbances) above or below water all have the potential to generate a tsunami. Unlike normal ocean waves, which are generated by wind, or tides, which are in turn generated by the gravitational pull of the Moon and the Sun, a tsunami is generated by the displacement of water from a large event.
Tsunami waves do not resemble normal undersea currents or sea waves because their wavelength is far longer. Rather than appearing as a breaking wave, a tsunami may instead initially resemble a rapidly rising tide. For this reason, it is often referred to as a tidal wave, although this usage is not favoured by the scientific community because it might give the false impression of a causal relationship between tides and tsunamis. Tsunamis generally consist of a series of waves, with periods ranging from minutes to hours, arriving in a so-called "wave train". Wave heights of tens of metres can be generated by large events. Although the impact of tsunamis is limited to coastal areas, their destructive power can be enormous, and they can affect entire ocean basins. The 2004 Indian Ocean tsunami was among the deadliest natural disasters in human history, with at least 230,000 people killed or missing in 14 countries bordering the Indian Ocean.
View the full Wikipedia page for TsunamiWave packet in the context of Group velocity
The group velocity of a wave is the velocity with which the overall envelope shape of the wave's amplitudes—known as the modulation or envelope of the wave—propagates through space.
For example, if a stone is thrown into the middle of a very still pond, a circular pattern of waves with a quiescent center appears in the water, also known as a capillary wave. The expanding ring of waves is the wave group or wave packet, within which one can discern individual waves that travel faster than the group as a whole. The amplitudes of the individual waves grow as they emerge from the trailing edge of the group and diminish as they approach the leading edge of the group.
View the full Wikipedia page for Group velocity