In physics Physics is a natural science that involves the study of matter and its motion through space-time, as well as all applicable concepts, including energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves, the wavelength of a sinusoidal wave The sine wave or sinusoid is a mathematical function that describes a smooth repetitive oscillation. It occurs often in pure mathematics, as well as physics, signal processing, electrical engineering and many other fields. Its most basic form as a function of time is: is the spatial period of the wave – the distance over which the wave's shape repeats.[1] It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a characteristic of both traveling waves and standing waves This phenomenon can occur because the medium is moving in the opposite direction to the wave, or it can arise in a stationary medium as a result of interference between two waves traveling in opposite directions. In the second case, for waves of equal amplitude traveling in opposing directions, there is on average no net propagation of energy, as well as other spatial wave patterns.[2][3] Wavelength is commonly designated by the Greek Greek , an independent branch of the Indo-European family of languages, is the language of the Greeks. Native to the southern Balkans, it has the longest documented history of any Indo-European language, spanning 34 centuries of written records. In its ancient form, it is the language of classical ancient Greek literature and the New Testament of letter A letter is an element in an alphabetic system of writing, such as the Greek alphabet and its descendants. Each letter in the written language is usually associated with one phoneme in the spoken form of the language lambda Lambda is the 11th letter of the Greek alphabet. In the system of Greek numerals lambda has a value of 30. Lambda is related to the Phoenician letter Lamed . Letters in other alphabets that stemmed from lambda include the Roman L and the Cyrillic letter El (Л, л). The ancient grammarians and dramatists give evidence to the pronunciation as /laː (λ). The concept can also be applied to periodic waves of non-sinusoidal shape.[1][4] The term wavelength is also sometimes applied to modulated In electronics, modulation is the process of varying one or more properties of a high frequency periodic waveform, called the carrier signal, with respect to a modulating signal. This is done in a similar fashion as a musician may modulate a tone from a musical instrument by varying its volume, timing and pitch. The three key parameters of a waves, and to the sinusoidal envelopes In mathematics, an envelope of a family of manifolds is a manifold that is tangent to each member of the family at some point of modulated waves or waves formed by interference In physics, interference is the addition of two or more waves that results in a new wave pattern. Interference usually refers to the interaction of waves that are correlated or coherent with each other, either because they come from the same source or because they have the same or nearly the same frequency. Interference in physics corresponds to of several sinusoids.[5]
Assuming a sinusoidal wave moving at a fixed wave speed, wavelength is inversely proportional to frequency Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency. The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency. Loosely speaking, 1 year is the period of the Earth's orbit around the Sun, and the Earth's rotation on its axis has: waves with higher frequencies have shorter wavelengths, and lower frequencies have longer wavelengths.[6]
Examples of wave-like phenomena are sound waves Sound is a travelling wave which is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations, light Light is electromagnetic radiation of a wavelength that is visible to the human eye . In physics, the term light sometimes refers to electromagnetic radiation of any wavelength, whether visible or not, and water waves In fluid dynamics wind waves, or more precisely wind generated waves, are surface waves that occur on the free surface of oceans, seas, lakes, rivers and canals — or even on small puddles and ponds. They usually result from the wind blowing over a vast enough stretch of fluid surface. Some waves in the oceans can travel thousands of miles before. A sound Sound is a travelling wave that is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations wave is a periodic variation in air pressure Sound pressure or acoustic pressure is the local pressure deviation from the ambient atmospheric pressure caused by a sound wave. Sound pressure can be measured using a microphone in air and a hydrophone in water. The SI unit for sound pressure p is the pascal (symbol: Pa), while in light Light is electromagnetic radiation of a wavelength that is visible to the human eye . In physics, the term light sometimes refers to electromagnetic radiation of any wavelength, whether visible or not and other electromagnetic radiation Electromagnetic radiation is a phenomenon that takes the form of self-propagating waves in a vacuum or in matter. It comprises electric and magnetic field components, which oscillate in phase perpendicular to each other and perpendicular to the direction of energy propagation. Electromagnetic radiation is classified into several types according to the strength of the electric In physics, an electric field is a property that describes the space that surrounds electrically charged particles or that which is in the presence of a time-varying magnetic field. This electric field exerts a force on other electrically charged objects. The concept of an electric field was introduced by Michael Faraday and the magnetic field Magnetic fields surround magnetic materials and electric currents and are detected by the force they exert on other magnetic materials and moving electric charges. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field vary. Water waves are periodic variations in the height of a body of water. In a crystal lattice vibration In physics, a phonon is a quasiparticle characterized by the quantization of the modes of lattice vibrations of periodic, elastic crystal structures of solids, atomic positions vary periodically in both lattice position and time.
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 in the water moves in a circle of the same diameter as the wave height, unrelated to wavelength.[7]
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Sinusoidal waves
In linear The word linear comes from the Latin word linearis, which means created by lines. In mathematics, a linear map or function f is a function which satisfies the following two properties: media, any wave 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:[8]
where v is called the phase speed (magnitude of the phase velocity The phase velocity of a wave is the rate at which the phase of the wave propagates in space. This is the speed at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave (for example, the crest) will appear to travel at the phase velocity. The phase speed is given in terms of the) of the wave and f is the wave's frequency.
In the case of electromagnetic radiation Electromagnetic radiation is a phenomenon that takes the form of self-propagating waves in a vacuum or in matter. It comprises electric and magnetic field components, which oscillate in phase perpendicular to each other and perpendicular to the direction of energy propagation. Electromagnetic radiation is classified into several types according to—such as light—in free space In classical physics, free space is a concept of electromagnetic theory, corresponding to a theoretically perfect vacuum and sometimes referred to as the vacuum of free space, or as classical vacuum, and is appropriately viewed as a reference medium, the phase speed is the speed of light The speed of light, usually denoted by c, is a physical constant important in many areas of physics. Light and all other electromagnetic radiation always travel at this speed in empty space , regardless of the motion of the source or the inertial frame of the observer. Its value is exactly 299,792,458 metres per second (approximately 186,282 miles, about 3×108 Scientific notation, also known as standard form or as exponential notation, is a way of writing numbers that accommodates values too large or small to be conveniently written in standard decimal notation. Scientific notation has a number of useful properties and is often favored by scientists, mathematicians and engineers, who work with such m/s. For sound waves Sound is a travelling wave which is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations in air, the speed of sound The speed of sound is the rate of travel of a sound wave through an elastic medium. In dry air at 20 °C , the speed of sound is 343 metres per second (1,125 ft/s). This equates to 1,236 kilometres per hour (768 mph), or about one kilometer in three seconds and about one mile in five seconds. This figure increases with temperature (equations are is 343 m/s (1238 km/h) (at room temperature and atmospheric pressure In chemistry, standard conditions for temperature and pressure are standard sets of conditions for experimental measurements, to allow comparisons to be made between different sets of data. The most used standards are those of the International Union of Pure and Applied Chemistry (IUPAC) and the National Institute of Standards and Technology (NIST)). As an example, the wavelength of a 100 MHz electromagnetic (radio) wave is about: 3×108 m/s divided by 100×106 Hz = 3 metres.
Visible light ranges from deep red Red is any of a number of similar colors evoked by light consisting predominantly of the longest wavelengths of light discernible by the human eye, in the wavelength range of roughly 630–740 nm. Longer wavelengths than this are called infrared , and cannot be seen by the naked human eye. Red is used as one of the additive primary colors of light,, roughly 700 nm A nanometre (Ancient Greek: νάνος, nanos, "dwarf"; μέτρον, metrοn, "unit of measurement") is a unit of length in the metric system, equal to one billionth of a metre, to violet As the name of a color, violet is used in two senses: first, referring to the color of light at the short-wavelength end of the visible spectrum, approximately 380–420 nm when indigo is recognized as a distinct color, or more commonly 380–450 nm (this is a spectral color). Second, violet may refer to a shade of purple, that is, a mixture of, roughly 400 nm (430–750 THz In physics, terahertz radiation refers to electromagnetic waves sent at frequencies in the terahertz range. It is also referred to as submillimeter radiation, terahertz waves, terahertz light, T-rays, T-light, T-lux and THz. The term is normally used for the region of the electromagnetic spectrum between 300 gigahertz and 3 terahertz (3x1012 Hz),) (for other examples, see electromagnetic spectrum The electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation. The "electromagnetic spectrum" of an object is the characteristic distribution of electromagnetic radiation emitted or absorbed by that particular object). The wavelengths of sound frequencies audible to the human ear (20 Hz The hertz is the SI unit of frequency defined as the number of cycles per second of a periodic phenomenon. One of its most common uses is the description of sine wave, particularly those used in radio and audio applications–20 kHz) are between approximately 17 m The metre , symbol m, is the base unit of length in the International System of Units (SI). Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole, its definition has been periodically refined to reflect growing knowledge of metrology. Since 1983, it is defined as the distance travelled by light in and 17 mm The millimetre is a unit of length in the metric system, equal to one thousandth of a metre, which is the SI base unit of length, respectively, assuming a typical speed of sound The speed of sound is the rate of travel of a sound wave through an elastic medium. In dry air at 20 °C , the speed of sound is 343 metres per second (1,125 ft/s). This equates to 1,236 kilometres per hour (768 mph), or about one kilometer in three seconds and about one mile in five seconds. This figure increases with temperature (equations are of about 343 m/s; the wavelengths in audible sound are much longer than those in visible light.
Frequency and wavelength can change independently, but only when the speed of the wave changes. For example, when light enters another medium, its speed and wavelength change while its frequency does not; this change of wavelength causes refraction Refraction is the change in direction of a wave due to a change in its speed. This is most commonly observed when a wave passes from one medium to another at an angle. Refraction of light is the most commonly observed phenomenon, but any type of wave can refract when it interacts with a medium, for example when sound waves pass from one medium, or a change in propagation direction of waves that encounter the interface between media at an angle.
Sinusoidal standing waves in a box that constrains the end points to be nodes will have an integer number of half wavelengths fitting in the box.Standing waves
A standing wave (black) depicted as the sum of two propagating waves traveling in opposite directions (red and blue).A standing wave This phenomenon can occur because the medium is moving in the opposite direction to the wave, or it can arise in a stationary medium as a result of interference between two waves traveling in opposite directions. In the second case, for waves of equal amplitude traveling in opposing directions, there is on average no net propagation of energy is an undulatory motion that stays in one place. A sinusoidal standing wave includes stationary points of no motion, called nodes A node is a point along a standing wave where the wave has minimal amplitude. For instance, in a vibrating guitar string, the ends of the string are nodes. By changing the position of the end node through frets, the guitarist changes the effective length of the vibrating string and thereby the note played. The opposite of a node is an anti-node, a, and the wavelength is twice the distance between nodes. The wavelength, period, and wave velocity are related as before, if the stationary wave is viewed as the sum of two traveling sinusoidal waves of oppositely directed velocities.[9]
Mathematical representation
Traveling sinusoidal waves are often represented mathematically in terms of their velocity v (in the x direction), frequency f and wavelength λ as:
where y is the value of the wave at any position x and time t, and A is the amplitude Amplitude is the magnitude of change in the oscillating variable with each oscillation within an oscillating system. For example, sound waves in air are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation. If a variable undergoes regular oscillations, and a graph of the system of the wave. They are also commonly expressed in terms of (radian) wavenumber Wavenumber is in the physical sciences a property of a wave proportional to the reciprocal of the wavelength. It can be defined as either k (2π times the reciprocal of wavelength) and angular frequency In physics, angular frequency ω is a scalar measure of rotation rate. Angular frequency (or angular speed) is the magnitude of the vector quantity angular velocity. The term angular frequency vector is sometimes used as a synonym for the vector quantity angular velocity ω (2π times the frequency) as:
in which wavelength and wavenumber are related to velocity and frequency as:
or
The relationship between ω and λ (or k) is called a dispersion relation Dispersion relations describe the ways that wave propagation varies with the wavelength or frequency of a wave. This variation has long explained how white light is dispersed into different colors, thus making rainbows possible. It turns out, thanks to the wave nature of all traveling objects, that dispersion relations are key to understand how. This is not generally a simple inverse relation because the wave velocity itself typically varies with frequency.[10]
Wavelength is decreased in a medium with higher refractive index.In the second form given above, the phase (kx − ωt) is often generalized to (k•r − ωt), by replacing the wavenumber k with a wave vector A wave vector is a vector which helps describe a wave. Like any vector, it has a magnitude and direction, both of which are important: Its magnitude is either the wavenumber or angular wavenumber of the wave (inversely proportional to the wavelength), and its direction is the direction of wave propagation that specifies the direction and wavenumber of a plane wave In the physics of wave propagation, a plane wave is a constant-frequency wave whose wavefronts (surfaces of constant phase) are infinite parallel planes of constant amplitude normal to the phase velocity vector in 3-space Three-dimensional space is a geometric model of the physical universe in which we live. The three dimensions are commonly called length, width, and depth , although any three mutually perpendicular directions can serve as the three dimensions, parameterized by position vector r. In that case, the wavenumber k, the magnitude of k, is still in the same relationship with wavelength as shown above, with v being interpreted as scalar speed in the direction of the wave vector. The first form, using reciprocal wavelength in the phase, does not generalize as easily to a wave in an arbitrary direction.
Generalizations to sinusoids of other phases, and to complex exponentials, are also common; see plane wave In the physics of wave propagation, a plane wave is a constant-frequency wave whose wavefronts (surfaces of constant phase) are infinite parallel planes of constant amplitude normal to the phase velocity vector. The typical convention of using the cosine phase instead of the sine phase when describing a wave is based on the fact that the cosine is the real part of the complex exponential in the wave
General media
The speed of a wave depends upon the medium in which it propagates. In particular, the speed of light in most media is lower than in vacuum, which means that the same frequency will correspond to a shorter wavelength in the medium than in vacuum. The wavelength in the medium is
where λ0 is the wavelength in vacuum, and n is the refractive index of the medium. When wavelengths of electromagnetic radiation are quoted, the vacuum wavelength is usually intended unless the wavelength is specifically identified as the wavelength in some other medium. In acoustics, where a medium is essential for the waves to exist, the wavelength value is given for a specified medium.
In general, the refractive index is a function of wavelength. This variation of n with λ, called dispersion, causes different colors of light to be separated when light is refracted by a prism.
Nonuniform media
A sinusoidal wave in a nonuniform medium, with loss. As the wave slows down, the wavelength gets shorter and the amplitude increases; after a place of maximum response, the short wavelength is associated with a high loss and the wave dies out.Wavelength can be a useful concept even if the wave is not periodic in space. For example, in an ocean wave approaching shore, shown in the figure, the incoming wave undulates with a varying local wavelength that depends in part on the depth of the sea floor compared to the wave height. The analysis of the wave can be based upon comparison of the local wavelength with the local water depth.[11]
Waves that are sinusoidal in time but propagate through a medium whose properties vary with position (an inhomogeneous medium) may propagate at a velocity that varies with position, and as a result may not be sinusoidal in space. The analysis of differential equations of such systems is often done approximately, using the WKB method (also known as the Liouville–Green method). The method integrates phase through space using a local wavenumber, which can be interpreted as indicating a "local wavelength" of the solution as a function of time and space.[12][13] This method treats the system locally as if it were uniform with the local properties; in particular, the local wave velocity associated with a frequency is the only thing needed to estimate the corresponding local wavenumber or wavelength. In addition, the method computes a slowly changing amplitude to satisfy other constraints of the equations or of the physical system, such as for conservation of energy in the wave.
Crystals
A wave on a line of atoms can be interpreted according to a variety of wavelengths.Waves in crystalline solids are not continuous, because they are composed of vibrations of discrete particles arranged in a regular lattice. This produces aliasing because the same vibration can be considered to have a variety of different wavelengths, as shown in the figure.[14] Descriptions using more than one of these wavelengths are redundant; it is conventional to choose the longest wavelength that fits the phenomenon. The range of wavelengths sufficient to provide a description of all possible waves in a crystalline medium corresponds to the wave vectors confined to the Brillouin zone.[15]
This indeterminacy in wavelength in solids is important in the analysis of wave phenomena such as energy bands and lattice vibrations. It is mathematically equivalent to the aliasing of a signal that is sampled at discrete intervals.
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Fri, 06 Aug 2010 11:02:54 GMT+00:00
Ars Technica First, the degree of polarization rotation depends on the wavelength of the light for most wavelengths, the effect is incredibly weak. ...
during travel
ue, 13 Jul 2010 14:12:29 GM
Two sinusoidal waves with equal wavelengths travel along a string in opposite directions at 3.0 m/s. The time between two successive instants when the antinodes are at maximum height is 0.25 s.What is the . wavelength. ?
Q. What is the wavelength and frequency of light? Does light have a short or long wavelength compated with radio waves?
Asked by humble.earthling - Tue Dec 25 20:39:19 2007 - - 9 Answers - 0 Comments
A. Wavelength of visible light varies from 400 to 700 nm, i.e., 4 x 10^(-7) to 7 x 10^(-7) m. This is much less than the wavelength of radio waves which can from a few cm to a few km. Frequency of visible light waves = velocity of light / wavelength = (3 x 10^8) / (4 x 10^(-7) = 7.5 x 10^16 Hz to = (3 x 10^8) / (7 x 10^(-7) = 4.3 x 10^16 Hz
Answered by Madhukar Daftary - Tue Dec 25 21:10:49 2007
