In the physics of wave propagation, a plane wave (also spelled planewave) is a constant-frequency wave whose wavefronts (surfaces of constant phase) are infinite parallel planes of constant peak-to-peak amplitude normal to the phase velocity vector.
It is not possible in practice to have a true plane wave; only a plane wave of infinite extent will propagate as a plane wave. However, many waves are approximately plane waves in a localized region of space. For example, a localized source such as an antenna produces a field that is approximately a plane wave far from the antenna in its far-field region. Similarly, if the length scales are much longer than the wave’s wavelength, as is often the case for light in the field of optics, one can treat the waves as light rays which correspond locally to plane waves.
Laser beams are also approximately planar. __TOC__
Two functions that meet the above criteria of having a constant frequency and constant amplitude are the sine and cosine functions. One of the simplest ways to use such a sinusoid involves defining it along the direction of the x-axis. The below equation, which is illustrated toward the right, uses the cosine function to represent a plane wave travelling in the positive x direction.
:In the above equation…
Other formalisms which directly use the wave’s wavelength , period , frequency and velocity are below.
:
:
:
To appreciate the equivalence of the above set of equations note that and
A more generalized form is used to describe a plane wave traveling in an arbitrary direction. It uses vectors in combination with the vector dot product.
: here: is the wave vector which only differs from a wave number in that it has a direction as well as a magnitude. This means that, . The direction of the wave vector is ordinarily the direction that the plane wave is traveling, but it can differ slightly in an anisotropic medium.
Many choose to use a more mathematically versatile formulation that utilizes the complex number plane. It requires the use of the natural exponent and the imaginary number .
:
To appreciate this equation’s relationship to the earlier ones, below is this same equation expressed using sines and cosines. Observe that the first term equals the real form of the plane wave just discussed.
: :
The complex form of the plane wave just introduced can be simplified by using a complex valued amplitude in place of the real valued amplitude . Specifically, since the complex form… : equals : one can absorb the phase factor into a complex amplitude by letting , resulting in the more compact equation :
While the complex form has an imaginary component, after the necessary calculations are performed in the complex plane, its real value can be extracted giving a real valued equation representing an actual plane wave.
:
The main reason one would choose to work with the complex exponential form of the plane wave is because complex exponentials are often algebraically easier to work with than the trigonometric sines and cosines. Specifically, the angle-addition rules are much simpler for complex exponentials.
Additionally, when using Fourier analysis techniques for waves in a lossy medium, the resulting attenuation is easier to deal with using complex Fourier coefficients. It should be noted however that if a wave is traveling through a lossy medium, the amplitude of the wave is no longer constant and therefore the wave is strictly speaking is no longer a true plane wave.
In quantum mechanics the solutions of the Schrödinger wave equation are by their very nature complex and in the simplest instance take a form identical to the complex plane wave representation above. The imaginary component in that instance however has not been introduced for the purpose of mathematical expediency but is in fact an inherent part of the “wave”.
These waves are solutions for a scalar wave equation in a homogeneous medium. For vector wave equations, such as the ones describing electromagnetic radiation or waves in an elastic solid, the solution for a homogeneous medium is similar: the ''scalar'' amplitude ''Ao'' is replaced by a constant ''vector'' Ao. For example, in electromagnetism Ao is typically the vector for the electric field, magnetic field, or vector potential. A transverse wave is one in which the amplitude vector is orthogonal to k, which is the case for electromagnetic waves in an isotropic medium. By contrast, a longitudinal wave is one in which the amplitude vector is parallel to k, such as for acoustic waves in a gas or fluid.
The plane-wave equation works for arbitrary combinations of ''ω'' and k, but any real physical medium will only allow such waves to propagate for those combinations of ''ω'' and k that satisfy the dispersion relation of the medium. The dispersion relation is often expressed as a function, ''ω''(k). The ratio ''ω''/|k| gives the magnitude of the phase velocity and ''dω''/''d''k gives the group velocity. For electromagnetism in an isotropic medium with index of refraction ''n'', the phase velocity is ''c''/''n'', which equals the group velocity if the index is not frequency-dependent.
In linear uniform media, a wave solution can be expressed as a superposition of plane waves. This approach is known as the Angular spectrum method. The form of the planewave solution is actually a general consequence of translational symmetry. More generally, for periodic structures having discrete translational symmetry, the solutions take the form of Bloch waves, most famously in crystalline atomic materials but also in photonic crystals and other periodic wave equations. As another generalization, for structures that are only uniform along one direction ''x'' (such as a waveguide along the ''x'' direction), the solutions (waveguide modes) are of the form exp[''i''(''kx''-''ωt'')] multiplied by some amplitude function ''a''(''y'',''z''). This is a special case of a separable partial differential equation.
The term is used in the same way for telecommunication, e.g. in Federal Standard 1037C and MIL-STD-188.
Represented in the second illustration is a circularly polarized, electromagnetic plane wave. Each blue vector indicating the perpendicular displacement from a point on the axis out to the helix, also represents the magnitude and direction of the electric field for an entire plane perpendicular to the axis.
In both illustrations, along the axes is a series of shorter blue vectors which are scaled down versions of the longer blue vectors. These shorter blue vectors are extrapolated out into the block of black vectors which fill a volume of space. Notice that for a given plane, the black vectors are identical, indicating that the magnitude and direction of the electric field is constant along that plane.
In the case of the linearly polarized light, the field strength from plane to plane varies from a maximum in one direction, down to zero, and then back up to a maximum in the opposite direction.
In the case of the circularly polarized light, the field strength remains constant from plane to plane but its direction steadily changes in a rotary type manner.
Not indicated in either illustration is the electric field’s corresponding magnetic field which is proportional in strength to the electric field at each point in space but is at a right angle to it. Illustrations of the magnetic field vectors would be virtually identical to these except all the vectors would be rotated 90 degrees perpendicular to the direction of propagation.
This text is licensed under the Creative Commons CC-BY-SA License. This text was originally published on Wikipedia and was developed by the Wikipedia community.
Coordinates | 38°37′38″N90°11′52″N |
---|---|
name | Tom Clancy |
birth date | May 12, 1947 |
birth place | Baltimore County, Maryland, United States |
occupation | Novelist |
nationality | American |
period | 1984–present |
genre | Techno-thriller, Crime fiction, nonfiction |
influences | H.P. Lovecraft, William Shakespeare, Eric Donovan, Robert A. Heinlein |
influenced | Dale Brown, James Wesley Rawles |
website | }} |
Clancy and his first wife Wanda married in 1969, separated briefly in 1995, and permanently separated in December 1996. Wanda Clancy filed for divorce in November 1998, which became final in 1999.
In 1993, Tom Clancy joined a group of investors that included Peter Angelos and bought the Baltimore Orioles from Eli Jacobs. In 1998, he reached an agreement to purchase the Minnesota Vikings, but had to abandon the deal because of the divorce settlement cost.
On June 26, 1999, Clancy married freelance journalist Alexandra Marie Llewellyn, whom he had met in 1997. Llewellyn is the daughter of J. Bruce Llewellyn, and a family friend of Colin Powell, who originally introduced the couple to each other.
In 2008, the use of Clancy's name was purchased by French video game manufacturer Ubisoft for an undisclosed sum. It will be used in conjunction with video games and related products such as movies, and books.
Some of his books bear dedications to Republican political figures, most notably Ronald Reagan. In his novels, countries portrayed as hostile to the United States include the former Soviet Union, Syria, China, Iran, India, and Japan while Russia, Egypt, Saudi Arabia, Kuwait, South Korea, Taiwan, Israel, Pakistan, and the United Kingdom are shown as close allies of the United States.
On September 11, 2001, Clancy was interviewed by Judy Woodruff on CNN. During the interview, he observed that Islam does not condone suicide. Among other observations during this interview, Clancy cited discussions he had with military experts on the lack of planning to handle a hijacked plane being used in a suicide attack and criticized the news media's treatment of the United States Intelligence Community. Clancy appeared again on PBS's ''Charlie Rose'', where he debated Senator and future Vice-Presidential candidate John Edwards.
Clancy has been a Life Member of the National Rifle Association since 1978. He is a Republican.
The first NetForce novel was adapted as a television movie, starring Scott Bakula and Joanna Going. The first Op-Center novel was released to coincide with a 1995 NBC television mini-series of the same name (Tom Clancy's Op-Center) starring Harry Hamlin and a cast of stars. Though the mini-series did not continue, the book series did, but it had little in common with the first mini-series other than the title and the names of the main characters.
With the release of ''The Teeth of the Tiger'', Clancy introduced Jack Ryan's son and two nephews who were main characters; these characters continue in one of his latest novels, ''Dead Or Alive''.
Clancy has written several nonfiction books about various branches of the U.S. armed forces (see non-fiction listing, below). Clancy has also branded several lines of books and video games with his name that are written by other authors, following premises or storylines generally in keeping with Clancy's works. These are sometimes referred to by fans as "apostrophe" books; Clancy did not initially acknowledge that these series were being authored by others, only thanking the actual authors in the headnotes for their "invaluable contribution to the manuscript".
In 1997, Clancy signed a book deal with Penguin Putnam Inc. (both part of Pearson Education), that paid him US$50 million for the world-English rights to two new books. He then signed a second agreement for another US$25 million for a four-year book/multimedia deal. Clancy followed this up with an agreement with Berkley Books for 24 paperbacks to tie in with the ABC television miniseries ''Tom Clancy's Net Force'' aired in the fall/winter of 1998. The Op-Center universe has laid the ground for the series of books written by Jeff Rovin, which was in an agreement worth US$22 million bringing the total value of the package to US$97 million.
In the order in which they occur in the storyline (and when they occur):
Starting with the following novel, the series becomes distinctly different from real history as noted below.
Study in Command
Other
Many of the games bearing the Clancy name have been very successful, spawning several sequels and expansions. It is unknown how much input Clancy has into the games.
World news media is a fictional news network that had been featured in many Tom Clancy's video games.
It has been said that an attempt will be made to merge the various series into one coherent universe (~2:40-3:30)
Clancy received an honorary doctorate in humane letters and delivered the commencement address at Rensselaer Polytechnic Institute in 1992, and has since worked a reference to the school into many of his main works.
Clancy is an honorary Yeoman Warder of The Tower of London holding the title "Supernumerary Yeoman". On the television show Ace of Cakes his wife commissioned, for his 60th birthday, a special cake in the shape of the Tower of London in acknowledgment of his status. In the episode, Tom Clancy referred to the ''Beefeaters'' as, "Just a terrific bunch of guys".
Category:1947 births Category:Living people Category:American military writers Category:American thriller writers Category:Baltimore Orioles owners Category:Loyola University Maryland alumni Category:Maryland Republicans Category:People from Calvert County, Maryland Category:Techno-thrillers Category:Writers from Maryland Category:Guggenheim Fellows Category:American spy fiction writers Category:National Rifle Association members
an:Tom Clancy az:Tom Klensi be-x-old:Том Клэнсі bg:Том Кланси cs:Tom Clancy de:Tom Clancy el:Τομ Κλάνσυ es:Tom Clancy eo:Tom Clancy fa:تام کلنسی fr:Tom Clancy gl:Tom Clancy ko:톰 클랜시 io:Tom Clancy it:Tom Clancy he:טום קלנסי lb:Tom Clancy hu:Tom Clancy mr:टॉम क्लॅन्सी ms:Tom Clancy nl:Tom Clancy ja:トム・クランシー no:Tom Clancy nn:Tom Clancy nds:Tom Clancy pl:Tom Clancy pt:Tom Clancy ro:Tom Clancy ru:Клэнси, Том simple:Tom Clancy sk:Tom Clancy fi:Tom Clancy sv:Tom Clancy ta:டாம் கிளான்சி th:ทอม แคลนซี tr:Tom Clancy uk:Том Кленсі zh:湯姆·克蘭西This text is licensed under the Creative Commons CC-BY-SA License. This text was originally published on Wikipedia and was developed by the Wikipedia community.
The World News (WN) Network, has created this privacy statement in order to demonstrate our firm commitment to user privacy. The following discloses our information gathering and dissemination practices for wn.com, as well as e-mail newsletters.
We do not collect personally identifiable information about you, except when you provide it to us. For example, if you submit an inquiry to us or sign up for our newsletter, you may be asked to provide certain information such as your contact details (name, e-mail address, mailing address, etc.).
When you submit your personally identifiable information through wn.com, you are giving your consent to the collection, use and disclosure of your personal information as set forth in this Privacy Policy. If you would prefer that we not collect any personally identifiable information from you, please do not provide us with any such information. We will not sell or rent your personally identifiable information to third parties without your consent, except as otherwise disclosed in this Privacy Policy.
Except as otherwise disclosed in this Privacy Policy, we will use the information you provide us only for the purpose of responding to your inquiry or in connection with the service for which you provided such information. We may forward your contact information and inquiry to our affiliates and other divisions of our company that we feel can best address your inquiry or provide you with the requested service. We may also use the information you provide in aggregate form for internal business purposes, such as generating statistics and developing marketing plans. We may share or transfer such non-personally identifiable information with or to our affiliates, licensees, agents and partners.
We may retain other companies and individuals to perform functions on our behalf. Such third parties may be provided with access to personally identifiable information needed to perform their functions, but may not use such information for any other purpose.
In addition, we may disclose any information, including personally identifiable information, we deem necessary, in our sole discretion, to comply with any applicable law, regulation, legal proceeding or governmental request.
We do not want you to receive unwanted e-mail from us. We try to make it easy to opt-out of any service you have asked to receive. If you sign-up to our e-mail newsletters we do not sell, exchange or give your e-mail address to a third party.
E-mail addresses are collected via the wn.com web site. Users have to physically opt-in to receive the wn.com newsletter and a verification e-mail is sent. wn.com is clearly and conspicuously named at the point of
collection.If you no longer wish to receive our newsletter and promotional communications, you may opt-out of receiving them by following the instructions included in each newsletter or communication or by e-mailing us at michaelw(at)wn.com
The security of your personal information is important to us. We follow generally accepted industry standards to protect the personal information submitted to us, both during registration and once we receive it. No method of transmission over the Internet, or method of electronic storage, is 100 percent secure, however. Therefore, though we strive to use commercially acceptable means to protect your personal information, we cannot guarantee its absolute security.
If we decide to change our e-mail practices, we will post those changes to this privacy statement, the homepage, and other places we think appropriate so that you are aware of what information we collect, how we use it, and under what circumstances, if any, we disclose it.
If we make material changes to our e-mail practices, we will notify you here, by e-mail, and by means of a notice on our home page.
The advertising banners and other forms of advertising appearing on this Web site are sometimes delivered to you, on our behalf, by a third party. In the course of serving advertisements to this site, the third party may place or recognize a unique cookie on your browser. For more information on cookies, you can visit www.cookiecentral.com.
As we continue to develop our business, we might sell certain aspects of our entities or assets. In such transactions, user information, including personally identifiable information, generally is one of the transferred business assets, and by submitting your personal information on Wn.com you agree that your data may be transferred to such parties in these circumstances.