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Basic Physics III Lecture 6

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Automatisierte Medienanalyse

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Erkannte Entitäten
Sprachtranskript
Below 2 days ago we talked about
Superposition principle and interference of waves and you might remember do this Program but the cast of that stimulates 2 ways with some phase shift between them shown in red blue and then the sound waves As shown in green MMS be change to these Differences we observe the a constructive destructive for partially destructive interference And they also talked about ways interfering with It's all reflection and we can stimulate that in this problem as well but reversed in 1 of those 1 of those 2 weeks and now you see that result in ways that looks like it's not travel a lot Rather it just vibrates back-and-forth and that's life This means Davis called was standing and that's exactly what happened wave reflects off 1 hand and Runs back Onto itself we can that demonstrate This strain that is fixed on 1 side and then that and excite goes Those migration path and those vibration patterns are often called vibration modes also and that characterize in this case since it's just 1 dimension by Regions which are rich will not cause Woods and regions that are doomed maximally which I called and head for example of this is the simplest case so-called fundamental mode we have an old only on the way and that fixed The maximum vibration in the middle of it So the next next highest mode is tool of those and time Max Vibration and Selena what's altogether 1 at each end and 1 in the Middle East and then fine and the next Parliament has Of 4 Knollwood socially and and so on and so on and off cause always at the end must be since those Points are fixed and therefore they can apply And each of those molds that has a frequency associated with are those are called natural resonant frequency is just like In the case of force How wanted motion year Fundamentals It is also called the 1st harmonic and be higher-order modes are called the 2nd the 3rd and 4th harmonic and those order modes also called Overtones And each 1 refers to such a pact so we can actually look at what is really a wavelength and frequency of Those Standing waves and you observe that these standing wave Because of me bond early conditions that that fixed Those who ends wave has defeat Inside A list this box Because of Ladies standing wave that looks like it's actually the these 1st over what on his 2nd harmonic where exactly 1 wavelength Efforts in the box but just want your we only get half way so Each Aristotle Imagine how the way it would look like old site the area where it's really defined I don't think this picture him and we have a
The fundamental mode here we imagined that Continues Like this the visitor Now the role and you have no role but Of course But also the same distance he and we see that The lavender Kuwaitis River repeats itself is actually tulip And since this is a fundamental mode where we call this number 1 and you can also say this is to 1 if he now look
Uh told them that for the year 2nd harmonic 1st of all what their fate Exactly 1 inside the box and get A down the 2 equals pulled 2 and that this is actually a general formula Harmonic will have a wavelength Described White The length of the divided by a B was off so for example for the year of the 3rd harmonic we get One-and-a-half wavelengths Provisions inside box or wave And this twice the length divided let me now calculated an example of to make this
More practical so let's assume we have a piano strings and piano stringers 1 . 1 meters long and it has a mass of 9 grams and the question is How much attention is a must The string have so that its vibrating had a fundamental frequency 131 and a what other frequencies The 1st quarter harmonics And so I know the answer is therefore the fundamental mode recent everybody knows that the wavelength twice the length of the strain and since the string length is given as 1 . 1 meters that means that The wavelength There's 2 . 2 meters away from the wavelength of the fundamental we of course also nor the the frequency of fundamental constants given its 131 and from those tool we can find A wave velocity because that is as usual The product of frequency and later and multiply will numbers we get A 288 leaders sec we also know we had linear Marstons because muscle strain is given us Now ran the length of the string of 1 . 1 meters and so we can divide the mask of 0 . 0 0 9 kilograms by a length of the 1 . 1 meters and get Zia Ponzio 8 1 8 kilograms And now we can use re-creations of relates
Velocity and F-4 and tension Marston city so we have velocities Graham equals these tensions divided by the Marston city and that means that the tension force must be the master times A key velocities square
We've already calculated velocities All you have to do is plug in in the numbers and get But Tension force must be be 618 so not to the beach part of the problem what we are frequencies of the 1st 4 harmonics and
To do that These 1st observed That's where we had all formula for the wavelength the harmonics Monday to express that and units of frequencies so we are not that the wavelength of the any harmonic theirs Twice the length of the world Divided by the order of the mother of the harmonica and know that the product Laughter We wavelength of the and tell Monarch times the frequency and long must be be equal to The velocity of the way And therefore we console for arguing frequency of wheat and harmonic and The velocity divided by The wavelength and if we are locked in a is creation of the baguette We divided by 2 Al multiplied And so this is the frequency of the air
1st harmonic fundamental and this is the order of the harmonic so all we have to do is have Multiplying frequency of These fundamental with the order off A harmonic long look and fundamental frequencies already given that 131 so our That's already 1 result For the next 1 is just prices Much of wanted sticks to its 3rd orders 3 on the line between The change could fall Chow Monica the Solheim not Mathematical representation of The standing And seen From these from this demonstration program tasked with you can think of standing wave traveling with a somewhat traveling wave moving the left plus Traveling wave moving with the right solar be there we therefore say that We have to wait to assign a 1 looks like signed X minus on and 1 looks like KX plus on Monday at those 2 together In order to do that Exploit trigonometric identity that Some all signed Signed wine equals twice the sign of one-half of experts tends to call son of 1 of 6 miners what is 1 of the year many trigonometric identities And very was that on some of those waves which looks like this We get twice the amplitude and then The some more Those school terms inside the sign punch divided by Is simply KX so signed KEX and the uh the difference of those 2 arguments of the sine function is just Omega team to shoulder the little bit of a law clearly we have
X equals K plus Omega and white people's KKX miners on
Some X plus Y equals to X if 0 Elias Track the from each of the next minus wine equals 2 on In this summer we actually seperate Racial dependents All of the way from the time dependence on that Exactly what it looks like standing because Can't describes There are no Watson can't handle and this just described harmonic motion vibrational And now weekend have a reform Requirement that he's standing with Must fit inside Currently the box office that Signed off They equals 0 cases And that means that KAL must be equal I had to sleep All clients on And Taint in between KL equals tried to with tool and so on and since we know that OK it's too divided by Manitoba can also say this corresponds to an X equals slammed We learned for heartland for so on and view Rick for and notes to recovered from Seoul at Adelaide phenomenon which were not Cover and In this class our latest in this We the phase velocity is not a constant but it depends on the yeah on the frequency of the year of the way and if you remember another demonstration program to test the show Last month which
Show that you can represent Are basically almost an arbitrary shape A building and up from my assigned waves The with different frequencies like Chris For example the sort if we have such a dispersion but waves speed It's different depending on on the on the frequency Then there those Shapes storms remained intact but we will change the former leader Troubles in essence what it means that Chances washed out Door Dusseldorf disappeared and that is Why this phenomenon Scholar is then add another interesting phenomenon that Probably most people would could name and they think of ways on the breaking waves and all the ways out So do the Member break and also our shock waves like what happens when the train goes the song and those out to difficult behaviors of nonlinear waves much hotter handled in this The phase Velocity depends on the MP for example you can order a model breaking of always by your some some pulse and
This Part moves faster than this In this house will Charlton And eventually a global basis and then we really collapses
And in that There is often chaotic motion a nonlinear laser appeared in the air Many real-life situations including traffic jams Example but Are This so that announced some RISC a Chapter 15 vote so 1st of all are the sources of The waves Our vibrating objects so the vibration of the object Doesn't travel but I'm excited wave Their troubles all bought from such race can be single pulses Or they can be continues like a like signed A wavelength lambasted distance from wave crest wave crest of waves Try afterward trompe have assigned late for example
This 1 would be alarmed on respond with top response would be alarmed over this does distance affects the frequency is the mumbles
A wave length or Press a passing unit time we have the tools The maximum deviation from equilibrium for that hide from the equilibrium level to the crest worked with trough a delay velocity is given by the product The frequency and so eventual kind of Both Waves Transposed waves and longitudinal Norway and the chance was waived the oscillations happened perpendicular to be directional Propagation and 4 Lombard told Nova a wave of those oscillations on apparel waste transport energy and we can define and intensity richest beverage Powell area and this intensity Is proportional to the square off on the case of three-dimensional waves his intensity decreases It's great The system Intensity is proportional 1 of the greatest square the aren't told top of overtures since intensity is also proportional to the amplitude
Is proportional Tool 1 0 with the assistance of the square so bows
The intensity and amplitude decreased 1 decreases linearly and 1 decreases the power to where can define a wave number as true pine divided by the way length a criminology told angle of frequency which is to high divided by period were too high Times the frequency assigned waivers Described by displacement as a function of position and time given by Chris Expression and which would signed off weighed on time position plus or minus angular frequency and time plus some angle fine and if it if it's a plus sign the the waiver struggling left and minor assignments coming from the right and we can also be expressed that Kate times Ex Plus minus T where are these the velocity of the wave since the velocity There's only divided airwaves passing through the same regional space at the same time that's the principle Possible position And in this edition quotes Ms. interference it can be constructive A destructive or possibly destructive depending on the phase difference between the way waves of reflect off objects and in that reflection than the angle of Reflection equals Campbell incidents ways Also I changed direction when they encounter a bomb Rim with different ways velocity and in that There are a lot of refraction is that the racial The sign of the incident and we hope will be a sign of refracted waves equals he a ratio of Please Finally waste can do a 3rd thing fool around obstacles all diffract in that they also changed direction and the angle of the Direction changes is polyps the wavelength divided by the size of the object this is just a rough figures rough rule of thumb When waves in the field with the old reflection them standing waves can be produced If conditions are right and these appeal as it is Corporations which appeared to stand still And are several such vibration patterns of molds are possible and and standing waves A standing waves Fokker only Resonance frequencies The system and the lowest of Bones Resonance frequencies The fundamental the others are called tones they also ordered and labeled as Harmonics a Knollwood's all regions The out our predictions And the and panels of regions of maximum rich and if you have a quarter of Length Both fixed on both sides of the wavelength of The and harmonic is is given by lumber and equals to al always level and For the frequency of Some of the and harmonic is aimed Times We will Lossett divided twice at the removed Chula through Chapter 16 which applies Please waves to something are very familiar with and that a sound so 1st of all our there was sort of pool leanings When we say sound 1 Mr. 1 meaning is simply a physical sensation that head yours That has Something to do with how halt years built in addition to the physics of assist or they can mean that ditch would not pressure waves Which are produced physicals For sound to be heard I really need A tool 3 6 1st in need A source close Vibrating objects than need a medial that transports the entry of the Corporation for example and Finally we need some kind of a detector for example old years but we could also use Michael for thee wave intensity is related to the sensation offer Lalmas the wave frequency is related to the sensational which uh as far as their pitchers concert
A few years usually audible range He goes on between about 20 up to 20 thousand And That of course various person by a person and as you grow older typically The higher end of That audible range tends to become smaller older people usually only up to add 10 thousand beyond the audible range and if it's above we call it or ultrasound And efforts Below and call Interest that's not talk about the need that a big wave velocity sound waves in Yeah Is roughly 300 and the 31 degrees if we and 31 meters per 2nd at 0 degrees and then you correct . 6 meters per 2nd for every Degrees above freezing So for room temperature are about 20 degrees Celsius For those conditions song speed about 343 So this on speed depends on the At like temperature is also different Different media some property it and other media than just So for example if you There desk with the sounds be basically triples And it is even faster and hydrogen gas In general and these sounds leaders Slower gasses and fast and liquids And it's the fastest And insult And see that Hong This little table so let me start with the 1st examples of you probably are very familiar with the wolf Some that helped to estimate poll Follow a thunderstorm as simply by observing the time between the scene a flash of lightning and hearing the sound of the rule of thumb was that It was a distance off A thunderstorm of 1 mile for every 5 seconds before the founders And can that easy Explained that Knowing the value of the sound speed 1st of all We note that the light speed is very fast of 300 thousand kilometers and so we can neglect any time elapsed between light happening and Are seen as these solid waste produced by the sound of troubles in 5 seconds at a distance of our typically about 1715 just simply part 2nd stands on the for of the 2nd And mile is 1609 needles which is fairly close to 1750 were found And therefore we found a song with troubles About 1 mile an hour seconds and therefore we can estimated what was the distance But All the time difference between an apparent time difference between flash and solar a sound waves on Monday poodle Norway's which means that Uh that the other molecules vibrate along the propagation she can for example Sine for sound this has usual on amplitude And sign off a wave number times X blindness and frequency Time will wave numbers tool Overlap and the angular frequencies to hide audit period Chg 1 can also considered a pressure leak and that produces priority variation off of the year Pressure And that can be represented by an Mathematically in this way we have some pressure on those times cosigned KX minds on So I tool further described a B sample it even for example a we need Additional dynamic ingredient and that is the so-called Baltimore a bulk modulus describes how compressible volume changes The new plant pressure So let's say they have some
Volume of Friday's some some pressure and becomes small From now on this 1 was the the volume leader of the Islamist avoiding me miners plus dealt with dollops years small and zeal then we would we can relate the ratio of the volume Change divided by 4 volume was originally due to the fact with the crap
Pressure Difference by constant which is called both Books and that's They're usually do with capital so let's not consider a particular type of war which is still in the area s and a thickness Doctors So if you now apply pressure on this on the lives of The soul of the then neither Delta X become slightly smaller distance of Delta D and we can then I find out hope because of this The distance by using the bulk modulus bear pressure change Delta Pete It is related to lower the volume change By I the bulk modulus of Delta peoples Mind Each times the surface area of time still divided by the surface Area times stopped Talks with Delta That is how much exchange we can write about our symbolically and after canceling all these surface area That Delta P should be the year of partial derivative of volume with respect With from not the volume Part of the rebuttable deed with respect to x and is in all our slogan creation of new parrot for sideways castle deemed equals favor times signed
X minus on And formed a derivative with respect to look X there is a constant change the sign becomes the coastline and pick up when extra fat off Haiti remains KX minus that he Seoul on a free men multiply with
A minus beat you get The pressure change as a function of position and time there be passed the bulk modulus times and food that has raised a number Times cosigned KX miners on the team And those expression in practices here this product of bulk modules and would raise that we can call the pressure Amplitude Dr. P. where Delta P M equals BACK So I what you observe if feud with that Is that while we all regional displacement was a times signed here on this pressure difference as a function Time Delta P M or pressure on the wound times the call sign of cakes mind on TV and that means that goes Tool waves have a phase difference between Seoul and that as indicated in this graph that at the bottom him so if look Displacement of a functional Time for example a position as euro we stopped Zero displacement but A B pressure Differences actually maximum at the lowest pressure You get the pressure difference pulled 1 back as a 90 degree phase shift between them between those 2 Description both descriptions are likable and how small if media make use Phase velocity which can be expressed The bulk modulus divided by volume density and that it's commodity That Mrs. Bruce similar to leave later velocity head on a role on the world they had a rates velocities where course the tension force divided by linear must end
New to clear And in the air for example have lost his career Equals the the bulk modulus divided by the volume so the linear density becomes the volume density tension force it's a replaced this Bob model Please that the same wall sort of keeping me he talked weekend next look at Vienna at the news this relations these free being roll
We can't War But Full beat new knowledge about modern roses These grip times and therefore this relation between pressure the food we get But the pressure the square times KA and then using the equals on our work paid replaces 1 of those To velocities The yield on the goal case and get We Pressure amplitude this Volume density times the velocity turns angular frequency time regular or if you wanna expressive in terms of our regular frequency angular frequency I have an extra factor Hi finally every look at the intensity In all from the previous chapter that The intensity is given by this Expression And we can now look but that expression And If you pick up on extra Rolled times The varsity both No orator the Norman Then there we get role the army decade in parentheses Graham which exactly expression pressure so the intensity is not just proportional Who am is also proportional put the pressure on square so as I said before on the description pressure equivalent of Description with displaced The only difference is that What we have This free factor for the intensity in the case of the displacement and put 8 get a different Our prefect of pressure Seoul at best a London the previous chapters the intensity is actually a B average Powell for surface area that is what a what intensity means The dollar was however a associated sensational typical human beings And a typical human being can pick up a solidly above 1 intensity of followed attentively minus 12 what square And that is called a rehearing special 0 and then became he has a sound waves 0 1 what the score 12 orders of magnitude Are bigger than this special every weekend here even out even beyond that then stocks become painful even so A fairly large range Rover sunken conflict could profitably be perceived by human beings factor of 10 12 And as it happens Our sensational loudness Not so much a proportional to the intensity but is proportionate with Margaret tents We therefore defined a so-called Luminous will sound level Plant To do that Bell invented General over with you it For a shirtless and it's called 1 hour 1 man and 1 Bell means of Basically a fractal 10 sold 1 basic build means 1 potential for 10 dB equals the 10 mathematically that means that Take the robber was of an intensity compare it to some reference I'm not and then multiplied by 10 and decibels And that gives us the sound level And for convenience There every pick for this reference value human healing I'm not So the air as it happens Sensitivity depends on the frequency So we care Also define allow this level and that it wanted of that is different it's called for and what it means is the same amount of decibels as if the frequency had been 1 thousand 4 years at Art typical curves for perceived developments for example he 20 formed as a function of frequency So if We have this Kind of intensity of the absolute sampler level of 60 dB this Frequency Bennett appears to to us when we listen to it On the ground 20 dB 1 thousand Therefore we say the loudness 24 so I will illustrate that the
Examples The next leg
Potenzialausgleich
Besprechung/Interview
Tonfrequenz
Wellenlänge
Schnittmuster
Kaliber <Walzwerk>
Abformung
Woche
Posament
Öffentliches Verkehrsmittel
Gießen <Urformen>
Armaturenbrett
Astronaut
Randspannung
Höhentief
Interferenzerscheinung
Schall
Wellenlänge
Massenresonanz
Tonfrequenz
Oberschwingung
Grün
Tag
Drachenpunkt
Druckkraft
Übungsmunition
TEM-Welle
Werkzeug
Elektromigration
Grundfrequenz
Reflexionskoeffizient
Mikrowelle
Jahr
Zylinderkopf
Öffentliches Verkehrsmittel
Lithium-Ionen-Akkumulator
Reflexion <Physik>
Wellenlänge
Weiß
Grundfrequenz
Oberschwingung
Längenmessung
Jahr
Mikrowelle
Drachenpunkt
TEM-Welle
Wellenlänge
Masse <Physik>
Oberschwingung
Stringtheorie
Besprechung/Interview
Tonfrequenz
Linearmotor
Sinterkörper
Stringtheorie
Cocktailparty-Effekt
Urkilogramm
Nanometerbereich
Druckkraft
Werkzeug
Grundfrequenz
Oberschwingung
Passfeder
Fahrgeschwindigkeit
Maske <Halbleitertechnologie>
Masse <Physik>
Randspannung
Myon
Wellenlänge
Grundfrequenz
Direkte Messung
Oberschwingung
Paarerzeugung
Tonfrequenz
Stringtheorie
Geldausgabeautomat
Druckkraft
Oberschwingung
Atmosphäre
Montag
Ersatzteil
Fahrgeschwindigkeit
Masse <Physik>
Instrumentenlandesystem
Oberschwingung
Bergmann
Tonfrequenz
Wellenlänge
Körner <Metallbearbeitung>
Stringtheorie
Kaliber <Walzwerk>
Leitungstheorie
Grundfrequenz
Weiß
Oberschwingung
Mikrowelle
Jahr
Montag
Herbst
Masse <Physik>
Amplitude
Personenzuglokomotive
Tonfrequenz
Stoßwelle
Summer
Sturm
Leisten
Tonfrequenz
Ladungstransport
Fahrgeschwindigkeit
Wellenlänge
Kaliber <Walzwerk>
Chirp
Gleiskette
Griff
Übungsmunition
Werkzeug
Schiffsklassifikation
Aktives Bauelement
Jahr
Mikrowelle
Modellbauer
Monat
Elementarteilchenphysik
Schwingungsphase
Abwrackwerft
Wellenlänge
Tonfrequenz
Basis <Elektrotechnik>
Rollsteig
Längenmessung
Crestfaktor
Astronom
Besprechung/Interview
Stoßdämpfer
Wellenlänge
Source <Elektronik>
Atmosphäre
Mikrowelle
Source <Elektronik>
Ersatzteil
Crestfaktor
Urkilogramm
Störsender
Laser
Sänfte
Schwingungsphase
Penumbra
Direkte Messung
Besprechung/Interview
Tonfrequenz
Wellenlänge
Energieniveau
Druckmaschine
Fahrgeschwindigkeit
Amplitude
Crestfaktor
Edelsteinindustrie
Wellenlänge
Kraft-Wärme-Kopplung
Crestfaktor
Verdrillung <Elektrotechnik>
Übungsmunition
Source <Elektronik>
Thermalisierung
Werkzeug
Negativer Widerstand
Licht
Mikrowelle
Intensitätsverteilung
Supernova
Longitudinalwelle
Bombe
Sensor
Konfektionsgröße
Besprechung/Interview
Tonfrequenz
Wellenlänge
Fahrgeschwindigkeit
Schnittmuster
Interferenz <Physik>
Auslenkung
Resonanzenergie
Schlauch
Korporale
Leistungssteuerung
Griff
Eisenkern
Wasserbeckenreaktor
Abformung
Reflexion <Physik>
Umlaufzeit
Lichtbrechung
Trenntechnik
Schalttafel
Himmel
Fahrgeschwindigkeit
Straßenbahn
Amplitude
Ton <Akustik>
Edelsteinindustrie
Höhentief
Schall
Wellenlänge
Rauschzahl
Druckmaschine
Source <Elektronik>
Werkzeug
Reflexionskoeffizient
Gleichstrom
Vollholz
Jahr
Mikrowelle
Source <Elektronik>
Intensitätsverteilung
Lineal
Ersatzteil
Anstellwinkel
Gewitter
Mikrowellentechnik
Temperatur
Uhr
Lichtgeschwindigkeit
Material
Kaliber <Walzwerk>
Regelstrecke
Kompressibilität
Montag
Druck
Amplitude
Längenmessung
Gewitter
Elektronische Medien
Druckmaschine
Werkzeug
Stuhl
Licht
Druckfeld
Jahr
Lineal
Elektronische Medien
Temperatur
Lunker
Leitrad
Bergmann
Besprechung/Interview
Tonfrequenz
Wellenlänge
Chirp
Nanometerbereich
Griff
Schall
Umlaufzeit
Druckluftanlage
Blitzeinschlag
Erdblitz
Stunde
Tonhöhe
Schall
Störlichtbogen
Proof <Graphische Technik>
Nadel
Gas
Source <Elektronik>
Flüssigkeit
Nassdampfturbine
Scheinbare Helligkeit
Ersatzteil
Rasterkraftmikroskop
Unterschallgeschwindigkeit
Wärmeaustauscher
Großkampfschiff
Längenmessung
Paarerzeugung
Besprechung/Interview
Wellenlänge
Satz <Drucktechnik>
Satzspiegel
Druckfeld
Jahr
Kompressibilität
Ersatzteil
Druck
Bergmann
Besprechung/Interview
A6M Zero-Sen
Auslenkung
Kompressibilität
Walzmaschine
Fahrgeschwindigkeit
Straßenbahn
Elementarteilchenphysik
Druck
Modulation
Gasdichte
Relativistische Mechanik
Zylinder <Maschinenbau>
Proof <Graphische Technik>
Druckkraft
Elektronische Medien
Druckmaschine
Kommode
Werkzeug
Atmosphäre
Schiffsrumpf
Druckfeld
Zylinderkopf
Mikrowelle
Modellbauer
Erder
Schaft <Waffe>
Durchführung <Elektrotechnik>
Tonfrequenz
Spannungsabhängigkeit
Energieniveau
Antiteilchen
Griff
Be-Stern
Range Rover
Regelstrecke
Stückliste
Fahrgeschwindigkeit
Amplitude
Absoluter Nullpunkt
Türglocke
Edelsteinindustrie
Schalldruck
Schreibstift
Stunde
Schall
Kaltumformen
Gasdichte
Relativistische Mechanik
Nivelliergerät
Druckmaschine
Übungsmunition
Atmosphäre
Druckfeld
Jahr
Leuchtdichte
Intensitätsverteilung
Schwellenspannung
Natürliche Radioaktivität
Walken <Textilveredelung>
Unterwasserfahrzeug

Metadaten

Formale Metadaten

Titel Basic Physics III Lecture 6
Serientitel Basic Physics III
Teil 6
Anzahl der Teile 26
Autor Smy, Michael
Lizenz CC-Namensnennung - Weitergabe unter gleichen Bedingungen 3.0 Unported:
Sie dürfen das Werk bzw. den Inhalt zu jedem legalen und nicht-kommerziellen Zweck nutzen, verändern und in unveränderter oder veränderter Form vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen und das Werk bzw. diesen Inhalt auch in veränderter Form nur unter den Bedingungen dieser Lizenz weitergeben.
DOI 10.5446/12942
Herausgeber University of California Irvine (UCI)
Erscheinungsjahr 2013
Sprache Englisch

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Fachgebiet Physik

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