Polarization is a property applying to transverse waves that specifies the geometrical orientation of the oscillations. In a transverse wave, the direction of the oscillation is perpendicular to the direction of motion of the wave. A simple example of a polarized transverse wave is vibrations traveling along a taut string. Depending on how the string is plucked, the vibrations can be in a vertical direction, horizontal direction, or at any angle perpendicular to the string. In contrast, in longitudinal waves, such as sound waves in a liquid or gas, the displacement of the particles in the oscillation is always in the direction of propagation, so these waves do not exhibit polarization. Transverse waves that exhibit polarization include electromagnetic waves such as light and radio waves, gravitational waves, transverse sound waves in solids. In some types of transverse waves, the wave displacement is limited to a single direction, so these do not exhibit polarization. An electromagnetic wave such as light consists of a coupled oscillating electric field and magnetic field which are always perpendicular.
In linear polarization, the fields oscillate in a single direction. In circular or elliptical polarization, the fields rotate at a constant rate in a plane as the wave travels; the rotation can have two possible directions. Light or other electromagnetic radiation from many sources, such as the sun and incandescent lamps, consists of short wave trains with an equal mixture of polarizations. Polarized light can be produced by passing unpolarized light through a polarizer, which allows waves of only one polarization to pass through; the most common optical materials are isotropic and do not affect the polarization of light passing through them. Some of these are used to make polarizing filters. Light is partially polarized when it reflects from a surface. According to quantum mechanics, electromagnetic waves can be viewed as streams of particles called photons; when viewed in this way, the polarization of an electromagnetic wave is determined by a quantum mechanical property of photons called their spin.
A photon has one of two possible spins: it can either spin in a right hand sense or a left hand sense about its direction of travel. Circularly polarized electromagnetic waves are composed of photons with only one type of spin, either right- or left-hand. Linearly polarized waves consist of photons that are in a superposition of right and left circularly polarized states, with equal amplitude and phases synchronized to give oscillation in a plane. Polarization is an important parameter in areas of science dealing with transverse waves, such as optics, seismology and microwaves. Impacted are technologies such as lasers and optical fiber telecommunications, radar. Most sources of light are classified as incoherent and unpolarized because they consist of a random mixture of waves having different spatial characteristics, frequencies and polarization states. However, for understanding electromagnetic waves and polarization in particular, it is easiest to just consider coherent plane waves. Characterizing an optical system in relation to a plane wave with those given parameters can be used to predict its response to a more general case, since a wave with any specified spatial structure can be decomposed into a combination of plane waves.
And incoherent states can be modeled stochastically as a weighted combination of such uncorrelated waves with some distribution of frequencies and polarizations. Electromagnetic waves, traveling in free space or another homogeneous isotropic non-attenuating medium, are properly described as transverse waves, meaning that a plane wave's electric field vector E and magnetic field H are in directions perpendicular to the direction of wave propagation. By convention, the "polarization" direction of an electromagnetic wave is given by its electric field vector. Considering a monochromatic plane wave of optical frequency f, let us take the direction of propagation as the z axis. Being a transverse wave the E and H fields must contain components only in the x and y directions whereas Ez = Hz = 0. Using complex notation, the instantaneous physical electric and magnetic fields are given by the real parts of the complex quantities occurring in the following equations; as a function of time t and spatial position z these complex fields can be written as: E → =
A beam is a structural element that resists loads applied laterally to the beam's axis. Its mode of deflection is by bending; the loads applied to the beam result in reaction forces at the beam's support points. The total effect of all the forces acting on the beam is to produce shear forces and bending moments within the beam, that in turn induce internal stresses and deflections of the beam. Beams are characterized by their manner of support, profile and their material. Beams are traditionally descriptions of building or civil engineering structural elements, but any structures such as automotive automobile frames, aircraft components, machine frames, other mechanical or structural systems contain beam structures that are designed to carry lateral loads are analyzed in a similar fashion. Beams were squared timbers but are metal, stone, or combinations of wood and metal such as a flitch beam. Beams can carry vertical gravitational forces but are used to carry horizontal loads; the loads carried by a beam are transferred to columns, walls, or girders, which transfer the force to adjacent structural compression members and to ground.
In light frame construction, joists may rest on beams. In carpentry, a beam is called a plate as in a sill plate or wall plate, beam as in a summer beam or dragon beam. In engineering, beams are of several types: Simply supported – a beam supported on the ends which are free to rotate and have no moment resistance. Fixed – a beam supported on both ends and restrained from rotation. Over hanging – a simple beam extending beyond its support on one end. Double overhanging – a simple beam with both ends extending beyond its supports on both ends. Continuous – a beam extending over more than two supports. Cantilever – a projecting beam fixed only at one end. Trussed – a beam strengthened by adding a cable or rod to form a truss. In the beam equation I is used to represent the second moment of area, it is known as the moment of inertia, is the sum, about the neutral axis, of dA*r^2, where r is the distance from the neutral axis, dA is a small patch of area. Therefore, it encompasses not just how much area the beam section has overall, but how far each bit of area is from the axis, squared.
The greater I is. Internally, beams subjected to loads that do not induce torsion or axial loading experience compressive and shear stresses as a result of the loads applied to them. Under gravity loads, the original length of the beam is reduced to enclose a smaller radius arc at the top of the beam, resulting in compression, while the same original beam length at the bottom of the beam is stretched to enclose a larger radius arc, so is under tension. Modes of deformation where the top face of the beam is in compression, as under a vertical load, are known as sagging modes and where the top is in tension, for example over a support, is known as hogging; the same original length of the middle of the beam halfway between the top and bottom, is the same as the radial arc of bending, so it is under neither compression nor tension, defines the neutral axis. Above the supports, the beam is exposed to shear stress. There are some reinforced concrete beams in which the concrete is in compression with tensile forces taken by steel tendons.
These beams are known as prestressed concrete beams, are fabricated to produce a compression more than the expected tension under loading conditions. High strength steel tendons are stretched; when the concrete has cured, the tendons are released and the beam is under eccentric axial loads. This eccentric loading creates an internal moment, and, in turn, increases the moment carrying capacity of the beam, they are used on highway bridges. The primary tool for structural analysis of beams is the Euler–Bernoulli beam equation; this equation describes the elastic behaviour of slender beams where the cross sectional dimensions are small compared to the length of the beam. For beams that are not slender a different theory needs to be adopted to account for the deformation due to shear forces and, in dynamic cases, the rotary inertia; the beam formulation adopted here is that of Timoshenko and comparative examples can be found in NAFEMS Benchmark Challenge Number 7. Other mathematical methods for determining the deflection of beams include "method of virtual work" and the "slope deflection method".
Engineers are interested in determining deflections because the beam may be in direct contact with a brittle material such as glass. Beam deflections are minimized for aesthetic reasons. A visibly sagging beam if structurally safe, is unsightly and to be avoided. A stiffer beam creates less deflection. Mathematical methods for determining the beam forces include the "moment distribution method", the force or flexibility method and the direct stiffness method. Most beams in reinforced concrete buildings have rectangular cross sections, but a more efficient cross section for a beam is an I or H section, seen in steel construction; because of the parallel axis theorem and the fact that most of the material is away from the neutral axis, the second moment of area of the beam increases, which in turn increases the stiffness. An I-beam is only the most efficient shape in one direction of be
In fluid dynamics, a wake may either be: the region of recirculating flow behind a moving or stationary blunt body, caused by viscosity, which may be accompanied by flow separation and turbulence, or the wave pattern on the water surface downstream of an object in a flow, or produced by a moving object, caused by density differences of the fluids above and below the free surface and gravity, or both. The wake is the region of disturbed flow downstream of a solid body moving through a fluid, caused by the flow of the fluid around the body. For a blunt body in subsonic external flow, for example the Apollo or Orion capsules during descent and landing, the wake is massively separated and behind the body is a reverse flow region where the flow is moving toward the body; this phenomenon is observed in wind tunnel testing of aircraft, is important when parachute systems are involved, because unless the parachute lines extend the canopy beyond the reverse flow region, the chute can fail to inflate and thus collapse.
Parachutes deployed into wakes suffer dynamic pressure deficits which reduce their expected drag forces. High-fidelity computational fluid dynamics simulations are undertaken to model wake flows, although such modeling has uncertainties associated with turbulence modeling, in addition to unsteady flow effects. Example applications include aircraft store separation. In incompressible fluids such as water, a bow wake is created when a watercraft moves through the medium; as with all wave forms, it spreads outward from the source until its energy is overcome or lost by friction or dispersion. The non-dimensional parameter of interest is the Froude number. Waterfowl and boats moving across the surface of water produce a wake pattern, first explained mathematically by Lord Kelvin and known today as the Kelvin wake pattern; this pattern consists of two wake lines that form the arms of a chevron, V, with the source of the wake at the vertex of the V. For sufficiently slow motion, each wake line is offset from the path of the wake source by around arcsin = 19.47° and is made up of feathery wavelets angled at 53° to the path.
The inside of the V is filled with transverse curved waves, each of, an arc of a circle centered at a point lying on the path at a distance twice that of the arc to the wake source. This pattern is independent of the speed and size of the wake source over a significant range of values. However, the pattern changes at high speeds, viz. above a hull Froude number of 0.5. As the source's speed increases, the transverse waves diminish and the points of maximum amplitude on the wavelets form a second V within the wake pattern, which grows narrower with the increased speed of the source; the angles in this pattern are not intrinsic properties of water: Any isentropic and incompressible liquid with low viscosity will exhibit the same phenomenon. Furthermore, this phenomenon has nothing to do with turbulence. Everything discussed here is based on the linear theory of an ideal fluid, cf. Airy wave theory. Parts of the pattern may be obscured by the effects of propeller wash, tail eddies behind the boat's stern, by the boat being a large object and not a point source.
The water need not be stationary, but may be moving as in a large river, the important consideration is the velocity of the water relative to a boat or other object causing a wake. This pattern follows from the dispersion relation of deep water waves, written as, ω = g k, where g = the strength of the gravity field ω is the angular frequency in radians per second k = angular wavenumber in radians per metre"Deep" means that the depth is greater than half of the wavelength; this formula implies that the group velocity of a deep water wave is half of its phase velocity, which, in turn, goes as the square root of the wavelength. Two velocity parameters of importance for the wake pattern are: v is the relative velocity of the water and the surface object that causes the wake. C is the phase velocity of varying with wave frequency; as the surface object moves, it continuously generates small disturbances which are the sum of sinusoidal waves with a wide spectrum of wavelengths. Those waves with the longest wavelengths have phase speeds above v and dissipate into the surrounding water and are not observed.
Other waves with phase speeds at or below v, are amplified through constructive interference and form visible shock waves, stationary in position w.r.t. The boat; the angle θ between the phase shock wave front and the path of the object is θ = arcsin. If c/v > 1 or < −1, no waves can catch up with earlier waves and no shockwave forms. In deep water, shock waves form from slow-moving sources, because waves with short enough wavelengths move slower; these shock waves are at sharper angles than one would naively expect, because it is group velocity that dictates the area of constructive interference and, in deep water, the group velocity is half of the phase velocity. All shock waves, that each by itself would have had an angle between 33° and 72°, are compressed into a narrow band of wake with angles between 15° and 19°, with the strongest constructive interference at the outer edge, placing the two arms of the V in the celebrated Kelvin wake pattern. A concise geometric construction demonstrates that, this group shock angle w.r.t.
The path of the boat
A rotation is a circular movement of an object around a center of rotation. A three-dimensional object can always be rotated around an infinite number of imaginary lines called rotation axes. If the axis passes through the body's center of mass, the body is said to rotate upon itself, or spin. A rotation about an external point, e.g. the Earth about the Sun, is called a revolution or orbital revolution when it is produced by gravity. The axis is called a pole. Mathematically, a rotation is a rigid body movement which, unlike a translation, keeps a point fixed; this definition applies to rotations within both two and three dimensions All rigid body movements are rotations, translations, or combinations of the two. A rotation is a progressive radial orientation to a common point; that common point lies within the axis of that motion. The axis is 90 degrees perpendicular to the plane of the motion. If the axis of the rotation lies external of the body in question the body is said to orbit. There is no fundamental difference between a “rotation” and an “orbit” and or "spin".
The key distinction is where the axis of the rotation lies, either within or outside of a body in question. This distinction can be demonstrated for "non rigid" bodies. If a rotation around a point or axis is followed by a second rotation around the same point/axis, a third rotation results; the reverse of a rotation is a rotation. Thus, the rotations around a point/axis form a group. However, a rotation around a point or axis and a rotation around a different point/axis may result in something other than a rotation, e.g. a translation. Rotations around the x, y and z axes are called principal rotations. Rotation around any axis can be performed by taking a rotation around the x axis, followed by a rotation around the y axis, followed by a rotation around the z axis; that is to say, any spatial rotation can be decomposed into a combination of principal rotations. In flight dynamics, the principal rotations are known as yaw and roll; this terminology is used in computer graphics. In astronomy, rotation is a observed phenomenon.
Stars and similar bodies all spin around on their axes. The rotation rate of planets in the solar system was first measured by tracking visual features. Stellar rotation is measured by tracking active surface features; this rotation induces a centrifugal acceleration in the reference frame of the Earth which counteracts the effect of gravity the closer one is to the equator. One effect is that an object weighs less at the equator. Another is that the Earth is deformed into an oblate spheroid. Another consequence of the rotation of a planet is the phenomenon of precession. Like a gyroscope, the overall effect is a slight "wobble" in the movement of the axis of a planet; the tilt of the Earth's axis to its orbital plane is 23.44 degrees, but this angle changes slowly. While revolution is used as a synonym for rotation, in many fields astronomy and related fields, revolution referred to as orbital revolution for clarity, is used when one body moves around another while rotation is used to mean the movement around an axis.
Moons revolve around their planet, planets revolve about their star. The motion of the components of galaxies is complex, but it includes a rotation component. Most planets in our solar system, including Earth, spin in the same direction; the exceptions are Uranus. Uranus rotates nearly on its side relative to its orbit. Current speculation is that Uranus started off with a typical prograde orientation and was knocked on its side by a large impact early in its history. Venus may be thought of as rotating backwards; the dwarf planet Pluto is anomalous in other ways. The speed of rotation is given by period; the time-rate of change of angular frequency is angular acceleration, caused by torque. The ratio of the two is given by the moment of inertia; the angular velocity vector describes the direction of the axis of rotation. The torque is an axial vector; the physics of the rotation around a fixed axis is mathematically described with the axis–angle representation of rotations. According to the right-hand rule, the direction away from the observer is associated with clockwise rotation and the direction towards the observer with counterclockwise rotation, like a screw.
The laws of physics are believed to be invariant under any fixed rotation. In modern physical cosmology, the cosmological principle is the notion that the distribution of matter in the universe is homogeneous and isotropic when viewed on a large enough scale, since the forces are expected to act uniformly throughout the universe and have no preferred direction, should, produce no observable irregularities in the large scale structuring over the course of evolution of the matter field, laid down by the Big Bang. In particular, for a system which behaves the same regardless of how it is oriented in space, its Lagrangian is rotationally invariant. According to Noether's theorem, if the action (the integral over ti
Noise-cancelling headphones, or noise-canceling headphones, are headphones that reduce unwanted ambient sounds using active noise control. This is distinct from passive headphones which, if they reduce ambient sounds at all, use techniques such as soundproofing. Noise cancellation makes it possible to listen to audio content without raising the volume excessively, it can help a passenger sleep in a noisy vehicle such as an airliner. In the aviation environment, noise-cancelling headphones increase the signal-to-noise ratio more than passive noise attenuating headphones or no headphones, making hearing important information such as safety announcements easier. Noise-cancelling headphones can improve listening enough to offset the effect of a distracting concurrent activity. To cancel the lower-frequency portions of the noise, noise-cancelling headphones use active noise control, they incorporate a microphone that measures ambient sound, generate a waveform, the exact negative of the ambient sound, mix it with any audio signal the listener desires.
Most noise-cancelling headsets in the consumer market generate the noise-cancelling waveform in real-time with analogue technology. In contrast, other active noise and vibration control products use soft real-time digital processing. To prevent higher-frequency noise from reaching the ear, most noise-cancelling headphones depend on soundproofing. Higher-frequency sound has a shorter wavelength, cancelling this sound would require locating devices to detect and counteract it closer to the listener's eardrum than is technically feasible or would require digital algorithms that would complicate the headphone's electronics. Noise-cancelling headphones specify the amount of noise they can cancel in terms of decibels; this number may be useful for comparing products but does not tell the whole story, as it does not specify noise reduction at various frequencies. By the 1950s, Dr. Lawrence Jerome Fogel created systems and submitted patents about active noise cancellation in the field of aviation; this system was designed to reduce noise for the pilots in the cockpit area and help make their communication easier and protect hearing.
Fogel was considered to be the inventor of active noise cancellation and he designed one of the first noise canceling headphones systems. On, Willard Meeker, designed an active noise control model, applied to circumaural earmuffs for advanced hearing protection. Noise-cancelling aviation headsets are now available. A number of airlines provide noise-cancelling headphones in their business and first class cabins. Noise cancelling is effective against aircraft engine noise. In these cases, the headphones are about the same size as normal headphones; the electronics, located in the plane handrest, take the sound from the microphone behind the headphone, invert it, add it back into the audio signal, which reduces background noise. Over the last few years, the use of noise-cancellation headphones as sleeping aids has increased. Both active and passive noise-cancellation headphones and ear plugs help to achieve better noise isolation from ambient sounds, helpful for people suffering from insomnia or other sleeping disorders, for whom sounds such as cars honking and snoring impact their ability to sleep.
For that reason, noise-cancelling sleep headphones and ear plugs are designed to cater to this segment of patients. Noise-cancelling headphones have the following drawbacks: They cost more than regular headphones. Active noise control requires power supplied by a USB port or a battery that must be replaced or recharged. Without power, some models do not function as regular headphones. Any battery and additional electronics may increase the size and weight of the headphones compared to regular headphones; the noise-cancelling circuitry may reduce audio quality and add high-frequency hiss, although reducing the noise may result in higher perceived audio quality. Active vibration control Noise-cancelling microphone Passive noise-cancelling headphones Throat microphone
Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure is the pressure relative to the ambient pressure. Various units are used to express pressure; some of these derive from a unit of force divided by a unit of area. Pressure may be expressed in terms of standard atmospheric pressure. Manometric units such as the centimetre of water, millimetre of mercury, inch of mercury are used to express pressures in terms of the height of column of a particular fluid in a manometer. Pressure is the amount of force applied at right angles to the surface of an object per unit area; the symbol for it is p or P. The IUPAC recommendation for pressure is a lower-case p. However, upper-case P is used; the usage of P vs p depends upon the field in which one is working, on the nearby presence of other symbols for quantities such as power and momentum, on writing style. Mathematically: p = F A, where: p is the pressure, F is the magnitude of the normal force, A is the area of the surface on contact.
Pressure is a scalar quantity. It relates the vector surface element with the normal force acting on it; the pressure is the scalar proportionality constant that relates the two normal vectors: d F n = − p d A = − p n d A. The minus sign comes from the fact that the force is considered towards the surface element, while the normal vector points outward; the equation has meaning in that, for any surface S in contact with the fluid, the total force exerted by the fluid on that surface is the surface integral over S of the right-hand side of the above equation. It is incorrect to say "the pressure is directed in such or such direction"; the pressure, as a scalar, has no direction. The force given by the previous relationship to the quantity has a direction, but the pressure does not. If we change the orientation of the surface element, the direction of the normal force changes accordingly, but the pressure remains the same. Pressure is distributed to solid boundaries or across arbitrary sections of fluid normal to these boundaries or sections at every point.
It is a fundamental parameter in thermodynamics, it is conjugate to volume. The SI unit for pressure is the pascal, equal to one newton per square metre; this name for the unit was added in 1971. Other units of pressure, such as pounds per square inch and bar, are in common use; the CGS unit of pressure is 0.1 Pa.. Pressure is sometimes expressed in grams-force or kilograms-force per square centimetre and the like without properly identifying the force units, but using the names kilogram, kilogram-force, or gram-force as units of force is expressly forbidden in SI. The technical atmosphere is 1 kgf/cm2. Since a system under pressure has the potential to perform work on its surroundings, pressure is a measure of potential energy stored per unit volume, it is therefore related to energy density and may be expressed in units such as joules per cubic metre. Mathematically: p =; some meteorologists prefer the hectopascal for atmospheric air pressure, equivalent to the older unit millibar. Similar pressures are given in kilopascals in most other fields, where the hecto- prefix is used.
The inch of mercury is still used in the United States. Oceanographers measure underwater pressure in decibars because pressure in the ocean increases by one decibar per metre depth; the standard atmosphere is an established constant. It is equal to typical air pressure at Earth mean sea level and is defined as 101325 Pa; because pressure is measured by its ability to displace a column of liquid in a manometer, pressures are expressed as a depth of a particular fluid. The most common choices are water; the pressure exerted by a column of liquid of height h and density ρ is given by the hydrostatic pressure equation p = ρgh, where g is the gravitational acceleration. Fluid density and local gravity can vary from one reading to another depending on local factors, so the height of a fluid column
In physics and related fields, a wave is a disturbance of a field in which a physical attribute oscillates at each point or propagates from each point to neighboring points, or seems to move through space. The waves most studied in physics are mechanical and electromagnetic. A mechanical wave is a local deformation in some physical medium that propagates from particle to particle by creating local stresses that cause strain in neighboring particles too. For example, sound waves in air are variations of the local pressure that propagate by collisions between gas molecules. Other examples of mechanical waves are seismic waves, gravity waves and shock waves. An electromagnetic wave consists of a combination of variable electric and magnetic fields, that propagates through space according to Maxwell's equations. Electromagnetic waves can travel through vacuum. Other types of waves include gravitational waves, which are disturbances in a gravitational field that propagate according to general relativity.
Mechanical and electromagnetic waves may seem to travel through space. In mathematics and electronics waves are studied as signals. On the other hand, some waves do not appear to move at all, like hydraulic jumps. Some, like the probability waves of quantum mechanics, may be static in both space. A plane seems to travel in a definite direction, has constant value over any plane perpendicular to that direction. Mathematically, the simplest waves are the sinusoidal ones. Complicated waves can be described as the sum of many sinusoidal plane waves. A plane wave can be transverse, if its effect at each point is described by a vector, perpendicular to the direction of propagation or energy transfer. While mechanical waves can be both transverse and longitudinal, electromagnetic waves are transverse in free space. Consider a traveling transverse wave on a string. Consider the string to have a single spatial dimension. Consider this wave as traveling in the x direction in space. For example, let the positive x direction be to the right, the negative x direction be to the left.
With constant amplitude u with constant velocity v, where v is independent of wavelength independent of amplitude. With constant waveform, or shapeThis wave can be described by the two-dimensional functions u = F u = G or, more by d'Alembert's formula: u = F + G. representing two component waveforms F and G traveling through the medium in opposite directions. A generalized representation of this wave can be obtained as the partial differential equation 1 v 2 ∂ 2 u ∂ t 2 = ∂ 2 u ∂ x 2. General solutions are based upon Duhamel's principle; the form or shape of F in d'Alembert's formula involves the argument x − vt. Constant values of this argument correspond to constant values of F, these constant values occur if x increases at the same rate that vt increases; that is, the wave shaped like the function F will move in the positive x-direction at velocity v. In the case of a periodic function F with period λ, that is, F = F, the periodicity of F in space means that a snapshot of the wave at a given time t finds the wave varying periodically in space with period λ.
In a similar fashion, this periodicity of F implies a periodicity in time as well: F = F provided vT = λ, so an observation of the wave at a fixed location x finds the wave undulating periodically in time with period T = λ/v. The amplitude of a wave may be constant, or may be modulated so as to vary with time and/or position; the outline of the variation in amplitude is called the envelope of the w