Travelling Wave

In a wave propagating in one direction, the particles of the medium travel progressively in the opposite direction, with such a gradation of speeds that the faster particles surpass the slower particles and are themselves overtaken by the faster particles.

A periodic travelling wave (also known as a wave train) in mathematics is a periodic function of one-dimensional space that moves at a constant speed and is defined as follows: As a result, it is a sort of spatiotemporal oscillation that is a periodic function of both space and time, which is distinct from the rest.

A crucial role in many mathematical equations is played by periodic travelling waves, which include self-oscillatory systems, excitable systems, and reaction-diffusion–advection systems. In biology, chemistry, and physics, equations of this type are frequently employed as mathematical models, and many empirical examples of phenomena resembling periodic travelling waves have been discovered.

Despite the fact that the mathematical theory of periodic travelling waves is most fully developed for partial differential equations, periodic travelling wave solutions can be found in a variety of other mathematical systems, including Integra differential equations, Integra difference equations, coupled map lattices, and cellular automata.

Periodic travelling waves are noteworthy in their own right, but they are also significant because they are the one-dimensional equivalent of spiral waves and target patterns in two-dimensional space, as well as the three-dimensional counterpart of scroll waves in three-dimensional space.

Travelling wave: An overview

When a vibrating object creates a disturbance, the wave travels across a medium, carrying energy with it as it goes. The mechanism by which a mechanical wave propagates in a medium involves particle contact; one particle pushes or pulls on its adjacent neighbour, causing that neighbour to be displaced from the equilibrium or rest position, and the process repeats itself. When a wave is viewed going through a medium, a crest can be seen moving from particle to particle along the path of the wave. There will be a trough after this crest and then another crest after that. This pattern will continue till the end of the cycle. In reality, a distinct wave pattern (in the shape of a sine wave) would be observed as it travelled through the medium. If the sine wave pattern encounters another wave along the medium’s length or if it encounters a boundary with another medium, it continues to flow in an uninterrupted manner. A travelling wave is a form of wave pattern that can be observed travelling through a medium and is sometimes referred to as such.

When a wave is not constrained to a certain space along a medium, travelling waves are found to exist. An ocean wave is the travelling wave that is most frequently witnessed. It is possible to confine a wave to a narrow location if it is injected into an elastic cable with its ends held 3 metres apart. A wave of this size has a maximum travel distance of only 3 metres. The wave will move fast to the other end of the cable, where it will reflect and return in the reverse manner. If there is a reflected portion of the wave, the section of the wave that is incident towards the fixed end will be interfered with. As a result of this interference, a new shape in the medium is created that is rarely similar to the shape of a sine wave. Therefore, no travelling wave is visible in the cable, despite the fact that it has been observed to pass through a medium in an unbroken form. Indeed, there are moving waves in the cord; it is simply that they are difficult to detect due to their interference with one another, which makes them difficult to detect. As a result, rather than viewing a pure sine wave pattern in the cable, an irregular and non-repeating pattern is created in the cord, which tends to change appearance over time as the cord is stretched. In this case, the irregular form is caused by the interference of a sine wave pattern from the incident source with a sine wave pattern from the reflected source in an untimely and non-sequenced fashion. Both the incident and reflected wave patterns continue their journey in the medium, meeting up with one another at various locations and in a variety of configurations. During the middle of the chord, for example, it may experience a crest meeting a half crest; then, seconds later, it may experience a crest meeting a quarter trough; and then, moments later, it may experience a three-quarters crest meeting a fifth trough, and so on. This interference results in an extremely irregular and non-repeating motion of the medium as a result of the interference. Because of the uneven motions of the individual particles, it is difficult to distinguish between the appearance of a true wave pattern and its absence.

Conclusion

A travelling wave is a transitory wave that generates a disturbance and travels along the transmission line at a constant speed while creating the disturbance. This type of wave only lasts for a brief period of time (a few microseconds), yet it causes a great deal of disruption in the line. The generation of the transient wave in the transmission line is mostly caused by switching, faults, and lightning.

It is essential to understand how the travelling wave works in order to know the voltages and currents at all places in the power system. These waves also aid in the design of insulators, protective equipment, the insulation of terminal equipment, and the overall coordination of insulation.