1.
Physics
–
Physics is the natural science that involves the study of matter and its motion and behavior through space and time, along with related concepts such as energy and force. One of the most fundamental disciplines, the main goal of physics is to understand how the universe behaves. Physics is one of the oldest academic disciplines, perhaps the oldest through its inclusion of astronomy, Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the mechanisms of other sciences while opening new avenues of research in areas such as mathematics. Physics also makes significant contributions through advances in new technologies that arise from theoretical breakthroughs, the United Nations named 2005 the World Year of Physics. Astronomy is the oldest of the natural sciences, the stars and planets were often a target of worship, believed to represent their gods. While the explanations for these phenomena were often unscientific and lacking in evidence, according to Asger Aaboe, the origins of Western astronomy can be found in Mesopotamia, and all Western efforts in the exact sciences are descended from late Babylonian astronomy. The most notable innovations were in the field of optics and vision, which came from the works of many scientists like Ibn Sahl, Al-Kindi, Ibn al-Haytham, Al-Farisi and Avicenna. The most notable work was The Book of Optics, written by Ibn Al-Haitham, in which he was not only the first to disprove the ancient Greek idea about vision, but also came up with a new theory. In the book, he was also the first to study the phenomenon of the pinhole camera, many later European scholars and fellow polymaths, from Robert Grosseteste and Leonardo da Vinci to René Descartes, Johannes Kepler and Isaac Newton, were in his debt. Indeed, the influence of Ibn al-Haythams Optics ranks alongside that of Newtons work of the same title, the translation of The Book of Optics had a huge impact on Europe. From it, later European scholars were able to build the devices as what Ibn al-Haytham did. From this, such important things as eyeglasses, magnifying glasses, telescopes, Physics became a separate science when early modern Europeans used experimental and quantitative methods to discover what are now considered to be the laws of physics. Newton also developed calculus, the study of change, which provided new mathematical methods for solving physical problems. The discovery of new laws in thermodynamics, chemistry, and electromagnetics resulted from greater research efforts during the Industrial Revolution as energy needs increased, however, inaccuracies in classical mechanics for very small objects and very high velocities led to the development of modern physics in the 20th century. Modern physics began in the early 20th century with the work of Max Planck in quantum theory, both of these theories came about due to inaccuracies in classical mechanics in certain situations. Quantum mechanics would come to be pioneered by Werner Heisenberg, Erwin Schrödinger, from this early work, and work in related fields, the Standard Model of particle physics was derived. Areas of mathematics in general are important to this field, such as the study of probabilities, in many ways, physics stems from ancient Greek philosophy
2.
Michael Faraday
–
Michael Faraday FRS was an English scientist who contributed to the study of electromagnetism and electrochemistry. His main discoveries include the principles underlying electromagnetic induction, diamagnetism, although Faraday received little formal education, he was one of the most influential scientists in history. It was by his research on the field around a conductor carrying a direct current that Faraday established the basis for the concept of the electromagnetic field in physics. Faraday also established that magnetism could affect rays of light and that there was a relationship between the two phenomena. He similarly discovered the principles of induction and diamagnetism. His inventions of electromagnetic rotary devices formed the foundation of electric motor technology, Faraday ultimately became the first and foremost Fullerian Professor of Chemistry at the Royal Institution of Great Britain, a lifetime position. James Clerk Maxwell took the work of Faraday and others and summarized it in a set of equations which is accepted as the basis of all theories of electromagnetic phenomena. The SI unit of capacitance is named in his honour, the farad, albert Einstein kept a picture of Faraday on his study wall, alongside pictures of Isaac Newton and James Clerk Maxwell. Faraday was born in Newington Butts, which is now part of the London Borough of Southwark but was then a part of Surrey. His family was not well off and his father, James, was a member of the Glassite sect of Christianity. James Faraday moved his wife and two children to London during the winter of 1790 from Outhgill in Westmorland, where he had been an apprentice to the village blacksmith, Michael was born in the autumn of that year. The young Michael Faraday, who was the third of four children, at the age of 14 he became an apprentice to George Riebau, a local bookbinder and bookseller in Blandford Street. During his seven-year apprenticeship Faraday read many books, including Isaac Wattss The Improvement of the Mind, at this time he also developed an interest in science, especially in electricity. Faraday was particularly inspired by the book Conversations on Chemistry by Jane Marcet, many of the tickets for these lectures were given to Faraday by William Dance, who was one of the founders of the Royal Philharmonic Society. Faraday subsequently sent Davy a 300-page book based on notes that he had taken during these lectures, davys reply was immediate, kind, and favourable. In 1813, when Davy damaged his eyesight in an accident with nitrogen trichloride, very soon Davy entrusted Faraday with the preparation of nitrogen trichloride samples, and they both were injured in an explosion of this very sensitive substance. In the class-based English society of the time, Faraday was not considered a gentleman, Faraday was forced to fill the role of valet as well as assistant throughout the trip. Davys wife, Jane Apreece, refused to treat Faraday as an equal, the trip did, however, give him access to the scientific elite of Europe and exposed him to a host of stimulating ideas
3.
Interference (wave propagation)
–
In physics, interference is a phenomenon in which two waves superpose to form a resultant wave of greater, lower, or the same amplitude. Interference effects can be observed with all types of waves, for example, light, radio, acoustic, surface water waves or matter waves. If a crest of a wave meets a crest of wave of the same frequency at the same point. If a crest of one wave meets a trough of another wave, constructive interference occurs when the phase difference between the waves is an even multiple of π, whereas destructive interference occurs when the difference is an odd multiple of π. If the difference between the phases is intermediate between two extremes, then the magnitude of the displacement of the summed waves lies between the minimum and maximum values. Consider, for example, what happens when two identical stones are dropped into a pool of water at different locations. Each stone generates a circular wave propagating outwards from the point where the stone was dropped, when the two waves overlap, the net displacement at a particular point is the sum of the displacements of the individual waves. At some points, these will be in phase, and will produce a maximum displacement, in other places, the waves will be in anti-phase, and there will be no net displacement at these points. Thus, parts of the surface will be stationary—these are seen in the figure above, prime examples of light interference are the famous Double-slit experiment, laser speckle, optical thin layers and films and interferometers. Dark areas in the slit are not available to the photons. Thin films also behave in a quantum manner, the above can be demonstrated in one dimension by deriving the formula for the sum of two waves. Suppose a second wave of the frequency and amplitude but with a different phase is also traveling to the right W2 = A cos where ϕ is the phase difference between the waves in radians. Constructive interference, If the phase difference is a multiple of pi. Interference is essentially a redistribution process. The energy which is lost at the interference is regained at the constructive interference. One wave is travelling horizontally, and the other is travelling downwards at an angle θ to the first wave, assuming that the two waves are in phase at the point B, then the relative phase changes along the x-axis. Constructive interference occurs when the waves are in phase, and destructive interference when they are half a cycle out of phase. Thus, a fringe pattern is produced, where the separation of the maxima is d f = λ sin θ
4.
Gliding
–
The word soaring is also used for the sport. Gliding as a sport began in the 1920s, initially the objective was to increase the duration of flights but soon pilots attempted cross-country flights away from the place of launch. Improvements in aerodynamics and in the understanding of phenomena have allowed greater distances at higher average speeds. Long distances are now flown using any of the sources of rising air, ridge lift, thermals. When conditions are favourable, experienced pilots can now fly hundreds of kilometres before returning to their home airfields, some competitive pilots fly in races around pre-defined courses. These gliding competitions test pilots abilities to make best use of weather conditions as well as their flying skills. Local and national competitions are organized in countries, and there are biennial World Gliding Championships. Techniques to maximize a gliders speed around the task in a competition have been developed, including the optimum speed to fly, navigation using GPS. If the weather deteriorates pilots are unable to complete a cross-country flight. Consequently, they may need to land elsewhere, perhaps in a field, powered-aircraft and winches are the two most common means of launching gliders. These and other methods require assistance and facilities such as airfields, tugs. These are usually provided by gliding clubs who also train new pilots, the development of heavier-than-air flight in the half century between Sir George Cayleys coachman in 1853 and the Wright brothers in 1903 mainly involved gliders. With the active support of the German government, there were 50,000 glider pilots by 1937, the first German gliding competition was held at the Wasserkuppe in 1920, organized by Oskar Ursinus. The best flight lasted two minutes and set a distance record of 2 kilometres. Within ten years, it had become an event in which the achieved durations. In 1931, Gunther Grönhoff flew 272 kilometres on the front of a storm from Munich to Kadaň in Western Czechoslovakia, in the 1930s, gliding spread to many other countries. In the 1936 Summer Olympics in Berlin gliding was a demonstration sport, a glider, the Olympia, was developed in Germany for the event, but World War II intervened. By 1939 the major gliding records were held by Russians, including a record of 748 kilometres
5.
Hydraulic jump
–
A hydraulic jump is a phenomenon in the science of hydraulics which is frequently observed in open channel flow such as rivers and spillways. When liquid at high velocity discharges into a zone of lower velocity, in an open channel flow, this manifests as the fast flow rapidly slowing and piling up on top of itself similar to how a shockwave forms. The phenomenon is dependent upon the fluid speed. If the initial speed of the fluid is below the critical speed, for initial flow speeds which are not significantly above the critical speed, the transition appears as an undulating wave. As the initial flow speed increases further, the transition becomes more abrupt, until at high enough speeds, when this happens, the jump can be accompanied by violent turbulence, eddying, air entrainment, and surface undulations, or waves. There are two main manifestations of hydraulic jumps and historically different terminology has been used for each, the different manifestations are, The stationary hydraulic jump – rapidly flowing water transitions in a stationary jump to slowly moving water as shown in Figures 1 and 2. The tidal bore – a wall or undulating wave of water moves upstream against water flowing downstream as shown in Figures 3 and 4. If considered from a frame of reference which moves with the wave front, a related case is a cascade – a wall or undulating wave of water moves downstream overtaking a shallower downstream flow of water as shown in Figure 5. If considered from a frame of reference which moves with the wave front and these phenomena are addressed in an extensive literature from a number of technical viewpoints. Hydraulic jumps can be seen in both a form, which is known as a hydraulic jump, and a dynamic or moving form. They can be described using the same approaches and are simply variants of a single phenomenon. A tidal bore is a jump which occurs when the incoming tide forms a wave of water that travel up a river or narrow bay against the direction of the current. Figure 3 shows a tidal bore with the common to shallow upstream water – a large elevation difference is observed. Figure 4 shows a tidal bore with the common to deep upstream water – a small elevation difference is observed. In both cases the tidal wave moves at the characteristic of waves in water of the depth found immediately behind the wave front. A key feature of tidal bores and positive surges is the turbulent mixing induced by the passage of the bore front. Another variation of the hydraulic jump is the cascade. In the cascade, a series of waves or undulating waves of water moves downstream overtaking a shallower downstream flow of water
6.
Saltstraumen
–
Saltstraumen is a small strait with one of the strongest tidal currents in the world. It is located in the municipality of Bodø in Nordland county and it is located about 10 kilometres southeast of the town of Bodø. The narrow channel connects the outer Saltfjorden to the large Skjerstad Fjord between the islands of Straumøya and Knaplundsøya, the Saltstraumen Bridge on Norwegian County Road 17 crosses Saltstraumen. Saltstraumen has one of the strongest tidal currents in the world, up to 400,000,000 cubic metres of seawater forces its way through a 3-kilometre long and 150-metre wide strait every six hours. Vortices known as whirlpools or maelstroms up to 10 metres in diameter and 5 metres in depth are formed when the current is at its strongest, Saltstraumen has existed for about two to three thousand years. Before that, the area was different due to post-glacial rebound, the current is created when the tide tries to fill Skjerstad Fjord. The height difference between the sea level and the fjord inside can be up to 1 metre, when the current turns, there is a period when the strait is navigable. The above account of the Saltstraumen is rather different than what The Norwegian Pilot reports, the Pilot’s description of the normal current is based on the time of the high tide at Bodø. The greatest southbound current occurs about one and a quarter hours before Bodø high tide, the speed of the current has a broad maximum being greater than six knots from three hours before Bodø high tide until half an hour after Bodø high tide. The greatest northbound current occurs about four and a half hours after Bodø high tide, when the outflowing current reaches over eight knots. The speed of this current also has a broad maximum being above six knots from two hours and forty minutes after Bodø high tide until five and a half hours before the next Bodø high tide. The behavior of the current may differ from normal due to winds or when more fresh water than usual is entering into the fjord from the surrounding mountains. Saltstraumen is popular with anglers, due to its abundance of such as saithe, cod, wolffish, rose fish. Coalfish is a specialty of the area, the largest documented coalfish of 22.7 kilograms was caught in Saltstraumen on a fishing rod. The first element is the name of the district Salten and the last element is the form of straum. The remains of a 10, 000-year-old hunter settlement in the area are the oldest known traces of settlement in Bodø. These hunters lived on the edge of the ice, attracted by the abundance of fish caused by the strong currents
7.
Transmission line
–
This article covers two-conductor transmission line such as parallel line, coaxial cable, stripline, and microstrip. Ordinary electrical cables suffice to carry low frequency alternating current, such as power, which reverses direction 100 to 120 times per second. However, they cannot be used to carry currents in the frequency range, above about 30 kHz, because the energy tends to radiate off the cable as radio waves. Radio frequency currents tend to reflect from discontinuities in the cable such as connectors and joints. These reflections act as bottlenecks, preventing the signal power from reaching the destination, Transmission lines use specialized construction, and impedance matching, to carry electromagnetic signals with minimal reflections and power losses. Types of transmission line include parallel line, coaxial cable, and planar transmission lines such as stripline, the higher the frequency of electromagnetic waves moving through a given cable or medium, the shorter the wavelength of the waves. Transmission lines become necessary when the length of the cable is longer than a significant fraction of the transmitted frequencys wavelength. At microwave frequencies and above, power losses in transmission lines become excessive, and waveguides are used instead, some sources define waveguides as a type of transmission line, however, this article will not include them. At even higher frequencies, in the terahertz, infrared and light range, waveguides in turn become lossy, mathematical analysis of the behaviour of electrical transmission lines grew out of the work of James Clerk Maxwell, Lord Kelvin and Oliver Heaviside. In 1855 Lord Kelvin formulated a model of the current in a submarine cable. The model correctly predicted the performance of the 1858 trans-Atlantic submarine telegraph cable. In 1885 Heaviside published the first papers that described his analysis of propagation in cables, in many electric circuits, the length of the wires connecting the components can for the most part be ignored. That is, the voltage on the wire at a time can be assumed to be the same at all points. Stated another way, the length of the wire is important when the signal frequency components with corresponding wavelengths comparable to or less than the length of the wire. A common rule of thumb is that the cable or wire should be treated as a line if the length is greater than 1/10 of the wavelength. If the transmission line is uniform along its length, then its behaviour is described by a single parameter called the characteristic impedance. This is the ratio of the voltage of a given wave to the complex current of the same wave at any point on the line. Typical values of Z0 are 50 or 75 ohms for a cable, about 100 ohms for a twisted pair of wires
8.
Ocean
–
An ocean is a body of saline water that composes much of a planets hydrosphere. On Earth, an ocean is one of the major divisions of the World Ocean. These are, in descending order by area, the Pacific, Atlantic, Indian, Southern, the word sea is often used interchangeably with ocean in American English but, strictly speaking, a sea is a body of saline water partly or fully enclosed by land. The ocean contains 97% of Earths water, and oceanographers have stated that less than 5% of the World Ocean has been explored, the total volume is approximately 1.35 billion cubic kilometers with an average depth of nearly 3,700 meters. As the world ocean is the component of Earths hydrosphere, it is integral to all known life, forms part of the carbon cycle. The world ocean is the habitat of 230,000 known species, but because much of it is unexplored, the origin of Earths oceans remains unknown, oceans are thought to have formed in the Hadean period and may have been the impetus for the emergence of life. Extraterrestrial oceans may be composed of water or other elements and compounds, the only confirmed large stable bodies of extraterrestrial surface liquids are the lakes of Titan, although there is evidence for the existence of oceans elsewhere in the Solar System. Early in their histories, Mars and Venus are theorized to have had large water oceans. The Mars ocean hypothesis suggests that nearly a third of the surface of Mars was once covered by water, compounds such as salts and ammonia dissolved in water lower its freezing point so that water might exist in large quantities in extraterrestrial environments as brine or convecting ice. Unconfirmed oceans are speculated beneath the surface of many planets and natural satellites, notably. The Solar Systems giant planets are thought to have liquid atmospheric layers of yet to be confirmed compositions. Oceans may also exist on exoplanets and exomoons, including surface oceans of water within a circumstellar habitable zone. Ocean planets are a type of planet with a surface completely covered with liquid. The concept of Ōkeanós has an Indo-European connection, Greek Ōkeanós has been compared to the Vedic epithet ā-śáyāna-, predicated of the dragon Vṛtra-, who captured the cows/rivers. Related to this notion, the Okeanos is represented with a dragon-tail on some early Greek vases, though generally described as several separate oceans, these waters comprise one global, interconnected body of salt water sometimes referred to as the World Ocean or global ocean. This concept of a body of water with relatively free interchange among its parts is of fundamental importance to oceanography. The major oceanic divisions – listed below in descending order of area and volume – are defined in part by the continents, various archipelagos, Oceans are fringed by smaller, adjoining bodies of water such as seas, gulfs, bays, bights, and straits. The Mid-Oceanic Ridge of the World are connected and form the Ocean Ridge, the continuous mountain range is 65,000 km long, and the total length of the oceanic ridge system is 80,000 km long
9.
Wavelength
–
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the waves shape repeats, and thus the inverse of the spatial frequency. Wavelength is commonly designated by the Greek letter lambda, the concept can also be applied to periodic waves of non-sinusoidal shape. The term wavelength is also applied to modulated waves. Wavelength depends on the medium that a wave travels through, examples of wave-like phenomena are sound waves, light, water waves and periodic electrical signals in a conductor. A sound wave is a variation in air pressure, while in light and other electromagnetic radiation the strength of the electric, water waves are variations in the height of a body of water. In a crystal lattice vibration, atomic positions vary, wavelength is a measure of the distance between repetitions of a shape feature such as peaks, valleys, or zero-crossings, not a measure of how far any given particle moves. For example, in waves over deep water a particle near the waters surface moves in a circle of the same diameter as the wave height. The range of wavelengths or frequencies for wave phenomena is called a spectrum, the name originated with the visible light spectrum but now can be applied to the entire electromagnetic spectrum as well as to a sound spectrum or vibration spectrum. In linear media, any pattern can be described in terms of the independent propagation of sinusoidal components. The wavelength λ of a sinusoidal waveform traveling at constant speed v is given by λ = v f, in a dispersive medium, the phase speed itself depends upon the frequency of the wave, making the relationship between wavelength and frequency nonlinear. In the case of electromagnetic radiation—such as light—in free space, the speed is the speed of light. Thus the wavelength of a 100 MHz electromagnetic wave is about, the wavelength of visible light ranges from deep red, roughly 700 nm, to violet, roughly 400 nm. For sound waves in air, the speed of sound is 343 m/s, the wavelengths of sound frequencies audible to the human ear are thus between approximately 17 m and 17 mm, respectively. Note that the wavelengths in audible sound are much longer than those in visible light, a standing wave is an undulatory motion that stays in one place. A sinusoidal standing wave includes stationary points of no motion, called nodes, the upper figure shows three standing waves in a box. The walls of the box are considered to require the wave to have nodes at the walls of the box determining which wavelengths are allowed, the stationary wave can be viewed as the sum of two traveling sinusoidal waves of oppositely directed velocities. Consequently, wavelength, period, and wave velocity are related just as for a traveling wave, for example, the speed of light can be determined from observation of standing waves in a metal box containing an ideal vacuum. In that case, the k, the magnitude of k, is still in the same relationship with wavelength as shown above
10.
Resonator
–
The oscillations in a resonator can be either electromagnetic or mechanical. Resonators are used to generate waves of specific frequencies or to select specific frequencies from a signal. Musical instruments use acoustic resonators that produce sound waves of specific tones, another example is quartz crystals used in electronic devices such as radio transmitters and quartz watches to produce oscillations of very precise frequency. A cavity resonator is one in which waves exist in a space inside the device. Acoustic cavity resonators, in sound is produced by air vibrating in a cavity with one opening, are known as Helmholtz resonators. A physical system can have as many resonant frequencies as it has degrees of freedom, systems with one degree of freedom, such as a mass on a spring, pendulums, balance wheels, and LC tuned circuits have one resonant frequency. Systems with two degrees of freedom, such as coupled pendulums and resonant transformers can have two resonant frequencies, a crystal lattice composed of N atoms bound together can have N resonant frequencies. As the number of coupled harmonic oscillators grows, the time it takes to transfer energy from one to the next becomes significant, the vibrations in them begin to travel through the coupled harmonic oscillators in waves, from one oscillator to the next. The term resonator is most often used for an object in which vibrations travel as waves, at an approximately constant velocity, bouncing back. The material of the resonator, through which the waves flow, therefore, they can have millions of resonant frequencies, although only a few may be used in practical resonators. The oppositely moving waves interfere with other, and at its resonant frequencies reinforce each other to create a pattern of standing waves in the resonator. If the distance between the sides is d, the length of a trip is 2 d. To cause resonance, the phase of a sinusoidal wave after a round trip must be equal to the initial phase so the waves self-reinforce. The above analysis assumes the medium inside the resonator is homogeneous, so the waves travel at a constant speed, and they are then called overtones instead of harmonics. There may be several such series of resonant frequencies in a single resonator, an electrical circuit composed of discrete components can act as a resonator when both an inductor and capacitor are included. Oscillations are limited by the inclusion of resistance, either via a specific resistor component, such resonant circuits are also called RLC circuits after the circuit symbols for the components. A distributed-parameter resonator has capacitance, inductance, and resistance that cannot be isolated into separate lumped capacitors, inductors, an example of this, much used in filtering, is the helical resonator. A single layer coil that is used as a secondary or tertiary winding in a Tesla coil or magnifying transmitter is also a distributed resonator
11.
Voltage
–
Voltage, electric potential difference, electric pressure or electric tension is the difference in electric potential energy between two points per unit electric charge. The voltage between two points is equal to the work done per unit of charge against an electric field to move the test charge between two points. This is measured in units of volts, voltage can be caused by static electric fields, by electric current through a magnetic field, by time-varying magnetic fields, or some combination of these three. A voltmeter can be used to measure the voltage between two points in a system, often a reference potential such as the ground of the system is used as one of the points. A voltage may represent either a source of energy or lost, used, given two points in space, x A and x B, voltage is the difference in electric potential between those two points. Electric potential must be distinguished from electric energy by noting that the potential is a per-unit-charge quantity. Like mechanical potential energy, the zero of electric potential can be chosen at any point, so the difference in potential, i. e. the voltage, is the quantity which is physically meaningful. The voltage between point A to point B is equal to the work which would have to be done, per unit charge, against or by the electric field to move the charge from A to B. The voltage between the two ends of a path is the energy required to move a small electric charge along that path. Mathematically this is expressed as the integral of the electric field. In the general case, both an electric field and a dynamic electromagnetic field must be included in determining the voltage between two points. Historically this quantity has also called tension and pressure. Pressure is now obsolete but tension is used, for example within the phrase high tension which is commonly used in thermionic valve based electronics. Voltage is defined so that negatively charged objects are pulled towards higher voltages, therefore, the conventional current in a wire or resistor always flows from higher voltage to lower voltage. Current can flow from lower voltage to higher voltage, but only when a source of energy is present to push it against the electric field. This is the case within any electric power source, for example, inside a battery, chemical reactions provide the energy needed for ion current to flow from the negative to the positive terminal. The electric field is not the only factor determining charge flow in a material, the electric potential of a material is not even a well defined quantity, since it varies on the subatomic scale. A more convenient definition of voltage can be found instead in the concept of Fermi level, in this case the voltage between two bodies is the thermodynamic work required to move a unit of charge between them
12.
Lee wave
–
In meteorology, lee waves are atmospheric stationary waves. The most common form is mountain waves, which are atmospheric internal gravity waves and these were discovered in 1933 by two German glider pilots, Hans Deutschmann and Wolf Hirth, above the Krkonoše. They can also be caused by the wind blowing over an escarpment or plateau. The vertical motion forces periodic changes in speed and direction of the air within this air current and they always occur in groups on the lee side of the terrain that triggers them. Usually a turbulent vortex, with its axis of rotation parallel to the range, is generated around the first trough. The strongest lee waves are produced when the lapse rate shows a layer above the obstruction, with an unstable layer above. Lee waves are a form of gravity waves produced when stably stratified flow is forced over an obstacle. This disturbance elevates air parcels above their level of neutral buoyancy, oscillations tilted off the vertical axis at an angle of ϕ will occur at a lower frequency of N cos ϕ. These air parcel oscillations occur in concert, parallel to the wave fronts and these wave fronts represent extrema in the perturbed pressure field, while the areas between wave fronts represent extrema in the perturbed buoyancy field. Energy is transmitted along the fronts, which is the direction of the wave group velocity. In contrast, the propagation of the waves points perpendicular to energy transmission. Waves may also form in dry air without cloud markers, Wave clouds do not move downwind as clouds usually do, but remain fixed in position relative to the obstruction that forms them. Around the crest of the wave, adiabatic expansion cooling can form a cloud in shape of a lens, multiple lenticular clouds can be stacked on top of each other if there are alternating layers of relatively dry and moist air aloft. The rotor may generate cumulus or cumulus fractus in its upwelling portion, the rotor cloud looks like a line of cumulus. It forms on the lee side and parallel to the ridge line and its base is near the height of the mountain peak, though the top can extend well above the peak and can merge with the lenticular clouds above. Rotor clouds have ragged edges and are dangerously turbulent. A foehn wall cloud may exist at the lee side of the mountains, a pileus or cap cloud, similar to a lenticular cloud, may form above the mountain or cumulus cloud generating the wave. Adiabatic compression heating in the trough of each wave oscillation may also evaporate cumulus or stratus clouds in the airmass, lee waves provide a possibility for gliders to gain altitude or fly long distances when soaring
This article incorporates public domain material from the General Services Administration document "Federal Standard 1037C".
This article incorporates 
