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Basic Physics III Lecture 7

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Automatisierte Medienanalyse

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Erkannte Entitäten
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The last time we talked about A solemn delays and the particular stopped of our 2 2 years found intensity And its relation to his sensational allowed so as said last time For a we have to distinguish Between the physical sensation and all brains From be physical phenomenon that was substance and because our Have evolved Range and intensity of Sound waves can seem Bayer Proportionally So I have to laugh That's just the way Are built and they can then define a number of units respond to do Brown and defined The dollar basis 10 some racial and then at 10 equals 1 Bell and therefore be if you wanna know the sound level for some particularly intensity I we compare it to Osama reference Intends to purchase usually taken as these human during threshold I'm not And it takes a lot the basis tens of this racial And then multiplied the 10 dB and that gives us Do you the sound level And here are some the girls sound levels for various noise All other songs sources for example a of a busy street traffic to get about 80 dB from if stand but close So jet Rain And you get 100 than 40 dB Intensities are listed next and humans are comfortable In the range offers decibels tool 100 after that I can still hear it becomes painful normally however will be shilling sensitivity also depends on the frequency of The song perceive so I these red curves on The sensitivity of the human years as a functional Frequencies for various as sound so if we hear about a hundred Hertz frequency That has a sound level of about 60 dB as it turns out there it sounds to us Aboard his as 40 dB sound level would About 1 killed and so find another unit which is called For That equalized bonds Basically You wanna know what is The form a particular song you listen to it You see how loud it sounds compared tool sound level 1 The maximum sensitivity in the near term beaches in the So there is now illustrates ozone levels with a few examples so let's say we are at a busy street corner and the sound level is a 75 decibels them what is the intensity of The actually intensity of the song The ready calculated that you date of the sound level 75 decibels and know that this is related to the intensity of the formula racial Iowa I'm not cannot Multiplied by 10 dB and a weekend bans for the lava just paid over 10 decibels or 7 . 5 and then we take The which is just 10 to the power of X so I know I'm not ratio 10 the power of 7 . 5 which is free point terms and now we use reference at level which is human he said during threshold or attend reminders of what And multiply this number I'm not and get A three-point 2 Times 10 to the minus 5 what square So that is how we would find an actual intensity from the sample little bits
Then consider another example the multiple sounds so let's say instead of street corner and we had a trumpeter Who plays the same sound level 75 And now me Equally trumpet players joined in what is sound level all The combined with solve that In all want trumpet player makes intensity I want the trees just computers and the sound level is is fatal equals locked and I want line not in orbit floor Trumpet players produced 4 times that intensity so I 4 equals 4 times and the sound level of It's just like his former replaced I want the war and since By 4 equals 4 times are 1 and did this And now we use the characteristics of The governor of function in particular the log 10 8
Times feed includes and they must lock Can't be solved in this case a equals and vehicles
I wonder why not so if you plug and then again at 10 decibels Locked and for small and I wonder why not Mr. missed Part multiplied terms that we already know what it's 70 Bulls This Part of every type calculated and arrival that the answer . 6 so we get their 6 dB added to 75 decibels and total found level was 81 So that is how I know that sounds not Much louder than a single try for the next thing we can considers Hollister sound intensity you behave as a function of distance of Dimensional On that The intensity proportional to 1 of the Rangers square for this is strictly not true enclosed rooms Because they're all reflections of some way off The wall walls at large distances Also some of the energy The song goes in air heating up the air so that's a dissipative Process That energy is lost the sound the intensity dropped faster than you would expect from 1 And higher frequencies experience more such losses This role Therefore we frequency spectrum of the song if changes at long distance However restrict ourselves to the proportional to the square Harold ensured for let's consider the jet Plane Again 30 meters has a sound level 140 decibels ignore our reflections of the ground the question is what is the sound level at 300 So we know that The intensity of a 300 meters is 100 times intensity of 30 meters 100 because it goes like 1 or distance square this 10 times the distance Therefore we intensity Must be 100 of the intensity of 30 we also know that These sound level at 50 meters 140 decibels Now sold in this Equation for me for the intensity of 300 meters and then plug and are formula for beta we get your Ponzio 1 times I've been derided by I'm not we do the same thing as that of the previous example so we used The feature of the with function So this time we have Add the garlic 10 or 0 . 0 1 with the song global leaders 10 to the policy of On 0 1 is minus 2 multiplied with 10 dB minus 20 dB at minus 20 dB the 140 decibels You get 120 which is still outside of a regional conflict for people even at a distance of 300 people let's consider stood example and that this illustrate how sensitive human years living off the let's calculated typical displacement of molecules sound having a frequency of around 1 thousand at a hearing Russia So what is the yeah Maximum pressure variation and what the maximum displacement of Emily So we have this hearing threshold of 10 to the minus 12 What that intensity we have given the frequency of 1000 The angular frequency of 6 thousand 280 feet per 2nd was yeah formula which relates The for the intensity and the frequency and we need to look up city from this is together and 1 . will 9 kilograms and we need the sound speed 340 meters so if guard amount sold for a not square When get A tool all our role or be kind intensity divided by ominous Graham those numbers The Ark Of the density of It The songs The frequencies The angular frequency greater than we come up with Displacement amplitude of 1 . 0 7 times 10 minus 11 This is the right time A typical after missile 10 to the minus 10 need for this that uh one-tenth of the size of 1 We guarantee can also calculated a maximum pressure over additional pressure to which related to displacement camps by by this On the other end We have to come up with a pressure operational tool . 9 7 times 10 to the minus part of the square A This is also a very tiny pressure reduction Yukon atmospheric pressure It about time for the past 5 years and you need a B a human years it's quite sensitive amazing nuisance because all the same problem also Differently but 1st going Pressure that we have this relation between the pressure The Food and intends to plant in the numbers Then we get there Are Pressure comfort food its 2 . 9 7 times turned on fire just Former terminology was again the relation between pressure The Food and based on and to get the displacement of costly arrived became the 1st 8 It'll be can't 1st displacement and toward 1st pressure Let me not talk about somewhat less quantifiable things that this Relations between frequency Fitch So ways that have trained all years It is The so-called equal templates scale which is a system of music and that made 1st made popular by Answer vast and about and divides on October into 12 after And the reason why it's called equally temple Because play any piece of music in every major or minor he result apparently to animals intervals And this is not Necessarily the case before the system was invented it could play out pieces of music only in certain he's played There are different keys and intervals Woodsong wrong and sometimes even this the absolute scale is Defined by 1st 80 should see this Don't here and let them on straight out of the songs
But a Thank you Some that some And the identifying this
They are now in the modern Times we identified as with 440 cycles per 2nd her soul an octave means at doubling the frequency And all the other at 12 tones Are defined with With those frequencies if want and the next October than you would also double those streak so really Ford was sound But Vibrating objects in particular by music instruments Nunavut strings columns um membrane metal would shape and typically Produced standing waves because those her natural resonance frequencies that either by striking plucking Boeing on in all of that The frequency of The vibrating object will be equal to the frequency of the weight they could for example for strain discussed these fundamental and had overtones We spare harmonic frequencies Became the object wavelength however there is still not the same as The wavelength of the wave of their size So for example lips stringed instruments of here on showing Tom and talk that can be role models by string fixed and all that
And Monaco That frequent And me over 12 this Is the way loss The string and almost the the length of the saw its Sarah talked to deliver the Tom because it's somewhat unwieldy broader locally here and We can Clark the strain And you hear about 1 particular note And now we can change the length of the string And we didn't get And will of course be shortened the length and therefore fundamental frequency becomes higher so the way we have plays such an instrument You change the length of the string the apparent length of the string President on fingers In between those threats and that is how we control the frequency and therefore be perceived pitch and She won't we change the tension But The What To Tarpley and also became just attention of those wireless
Dear old dad do In the moat tends to make good the height of the Richardson will be so 1 way off Losing string instruments at its plant in a however because there are some other time String Instruments for example violins along contrabass all such instruments Will be a standing wave succeeded in a different way to do that But users of both usually involving hair from the Taylor of course And moved here are across the strain and it produces some kind of a stick slip motion meaning that We hear sticks to the string and moved the horizontally Eventually the force Becomes too great and strain that goes back Equilibrium position but then grab again by him And what this But it with Singing kind of vibration that are particularly More pleasant than jogging shorts things like that so I'm most stringed instruments Actually we kind of mechanical amplifier for about 4 4 example of piano which is also an instrument that uses a sounding board and guitars and violence he said sounding box at the latest The talks process A transfer vibrations from large object which then has Most Area to set the air molecules of library the string would be itself Even so small instrument is not Particularly efficient and producing low-frequency sound much better at making higher frequencies on and that's simply has With the size of the instrument so if you want to efficiently frequencies Typically increase the size of the string as well as We are sounding so let's make an example of of Spring migration so let's Assume that have . Toledo long violence and that it is too late and above the the middle Cecil the 440 the question is What is the wavelength But The fundamental string of friction and what probably frequency and wavelengths of The that could and as usual gets these fundamental wavelength from twice String length for restraint and about On people will need meters so that means the wavelength of 0 . 6 4 4 already 1 And the solemn wave has the same frequency Nurse String of that's also warned The wavelength In Therefore on these Wait velocity of 340 meters per 2nd divided by 400 and that Gives us the wavelength here off the 0 . 7 8 which is different than the wavelength on the string And The reason why there's a difference between here and the wavelength on the strings that a wave pilosity on the strain is different from the velocity With velocity on the strain would be a 0 . 6 4 times for just wanted 18 Somewhat shorter than before and it would be the a 2nd we lost so let's next talk about wind instruments wind instruments on for example would wins Brown answers Pipe organs and they put was sounded a different they produce song former from vibrating here Itself so you typically you have to have column and the and excited at best Sending waves in those Corps and just let for the strain on displacement Notes and the way It's working out this that there would be pressure tool Actually it has an entire However the displacement No and by sea And unlike these strained it is possible that such Have both Ends Open or closed so let's 1st consider the case
Bob Of open to open on both sides of solar like this you have to have some air inside and the question is how can it vibrate and
In all that unlike further strengthen us nothing to prevent air molecules by here So any standing wave these will be areas of maximum vibration But In other words Displacement is going have and handled and them Perhaps you know Little Rock for any kind of way if you need to have at least 1 note therefore the fundamentalists at its given by an entire to and and by an old in the middle If you look at The pressure Instead of displacement then in all that He open and pressure must be equal surrounding pressure for that kind of life I like fixing the pressure Therefore we have pressure would and in the middle however there are precious Frito very And get them and handled in the middle and those 2 things that described the same vibration mode of the just A different ways of looking at the in both cases Land The wavelength of of this mode is Twice the length But you just like A these fundamental mode for raids on the street not be what tones As for the rates on the strain than and we get smaller and notes that and so forth This a 2nd harmonic so we get a tool displacement notes and a fleet displacement and panel or free pressure holds true pressure and time Parents They wavelength and this case Equal the length and so the formula for that relates wavelength And the length of the tube and be mode It's just the same I like it was on the street And always at the end of the displacement of maximum and handled and since pressures atmospheric That means that there must be oppression this is among between wave of air molecules Actually vibrating alongside 2 not did The 2nd case this summer that 1 end is open and honest close the case of both ends up close This is not useful for making an instrument because cannot excite anyway Inside and can't get out he saw a that The same will supply the open and we will get I'm an entire note for the displacement And an old for the pressure that had because and however we will get an old for the displacement of molecules and I'm an entire note for the pressure because you can get any arbitrary pressure This The formulas change the fundamental it's different and now we have only 1 quarter of wavelength in 2 and just like we imagine
The continuation for strength you can also imagine 2 of those uh chose to Start And If we haven't both of them the fundamental than we can complete 1 half of the wavelength so the total 1 new would be tools on not looks like there are opened to open at both And get the same formula for that for the fundamental however of course to actually produces only that we don't really need a bit the 2nd 1 and so we just imagine so that means that The member want equals 4 times the length of the tube 1 and disclosed 1 and now are Hugo till the old homes then then we cannot have a even tho he because
Putting an even would mean that we get displacement and Tylenol on top of pressure nor would it be closed end and that doesn't work for the 1st Old what Home that can fight The 3rd harmonic River get again displacement note and the pressure and had no clothes and from now we we get a three-quarters of a wavelength inside to Audi B 3rd harmonic wavelength 4 times the the length of the 2 divided by and so on with the 5th harmonic 4 times the length of the 2 divided by time And therefore these frequencies for the fundamental mode are given by the velocity of and for the 1st tone of the 3rd harmonic 3 times as much for the next 1 Part-time and Who demonstrates such their columns have really cheap toys this corresponds to open it to ends a new consort of sea that Because there's a whole lot The move his mood of food head Get a particular frequency and I can change the frequency by changing the apparent length of a column by opening and closing the fingering holes Breyer said They will So excited Sort of remember this Frequency All but 1 of the fingering was closed And a look at a different type of fuel and a sort of can measure the length And the longest 1 of those knee-length him is roughly one-half the length of this so if If a brilliant would expect that frequencies used doubled and that means a lot of time Pablo and sweat I recover the same and the reason for that is that at the bottom of those this type of and is actually closed and therefore Instead of be formula for both sides open have to apply the formula for once closer And that means that the fundamentals Fits in only a quarter of an hour therefore the frequencies will be Only half of what you would expect 1 with open on both so as I As for the would 1 controls The picture All the frequency by using Bingo halls Ridge Effective changes Had the length of the course was this Would be just use of different arm 1 selection legs enter Them from there is a 2nd trip However 1 can use the wind instruments And that is Instead of just opening and closing the fingering holes in sequins I can open the the 1st floor and if I do that Then I destroyed the vibrational travel in them but not necessarily for all of The molds possible destroyed for the fundamentals most of their corn and changed could opt to figures Alcock acres Barak and that is a technique called all which is used in many instruments for example quite excessive case from that is Also not tired of wind instruments that uses and I for 1 of them here which show you read looks The sewer readers is They are usually a piece of wood that cover the opening on on 1 side look at it from the side You see that there's a small gap between piece of wood and That should open And I want that That was used Closing off or pull it It basically controls the air flow into the instrument because we a piece of wood is then it is easy to bend it and if you don't worry not an instrument that it will just end away from the force and close the whole altogether if I applied a large pressure difference between my mouth instrument then I will get nowhere for of Gaza also get nowhere flawed but don't go in and All 4 0 pressure and somewhere in between there's a sweet spot where get the most fearful that little gaps and the way you operate Such a reed instrument that Go beyond this Maximum for example here and what happened Slightly different phenomenon residents as the air column Inside the instrument self excites stand in the way this looks like this Point aligned
I'm not this For my Former instrument with this 1 the opening so I have some pressure society Some pressure on both sides And if this Pressure at the inside this pressure inside happens to go up a little bit That means that the pressure difference witches P outside minus inside the pressure difference becomes smaller than on this On the scrap which relates pressure and with After this pressure difference becomes smaller that means we actually increased beer So streaming into the instrument and that means that pressure inside the instrument gets even higher and so this is sort of a runaway process until I exhausted be a reservoir of pressure On the outside which is not And that full of if I have a small fluctuations in the year the air pressure in this column Then it will be amplified by this Behavior off of the and
Given that a system highlights Standing wave media we get column will then controlled the week that the read write operations will produce a soft on demonstrated now Karen and which Street The young 1111 Oh yeah Shambley so if you look Clarinet and you wanna know what Kind of those 2 possible wind instrument is open Or closed And because of the read on 1 end its crew was on 1 hand and open on me there for this sound as The new law that produces compared to that of a fruitful Just like it was full of these for the compared with the regular the new novel a maker example for air columns So let's assume that you had 26 centimeters long All the time said 20 degrees Celsius and we won't know what This is a fundamental frequency Both sides are open on 1 side is close And in the case Off both sides opened in all of the fundamental frequency velocity in this case of are divided by twice the length or 343 meters the 2nd divided By 0 . 5 2 and meters and this Us the fundamental frequency of 616 if it's closed however then add the formula for the fundamental frequency The same velocity divided by What times The length and therefore instead of 660 we get 330 If you want to know what are the 1st lady overtones About the fundamental frequency than in the open cases as they Although tones are possible so tool across Britain on the trend that 3 equals 1980 and therefore equals 2 thousand 600 Ford If 1 closed then even numbers are not possible and you get for the 1st 3 or what Forms A beat equals triple the freedom that comes ought to be 989 then at 5 1615 and at 7 2 thousand 310 Let me know I talk about a different feature music instruments and listen to music instruments than that tend to be able to identifying instrument even if you don't see because each 1 has its own character so this is often referred to as Home color of Tomba sound called and that is in addition to the picture of the instrument and 1 can understand that By looking at these so-called so-called songs spectrum Turns out excite instrument excite standing race on an instrument you don't just excited to be fundamental usually excite some of these Tones of well and these are among the overtones that you get differs from instrument to instrument for example if back to him to this song
The Her father promised Lewis tends to use tends to sample people final On entertainment playing I'm not On the other hand if a Flute trailer name said It has its own slightly metal all over place time hairs than its doors a stone cold and the continuous spectrum would be heard not his So he some songs there From the key instruments the clarinet Earlier look something like this The piano makes like rat But And the violin now looks like that And way of course want you can hear those differences Is that news Some harmonics together When you get a different shape Of the waves and audio able to analyze shape And so we cover which which would you and it's quite good at it there's a lot of normal processing going on for some instruments as it turns out that These fundamentalists although an told that can't even all that is the case that typically run your players to were human being he will identify that as picture of the you know the fundamental is all but in the case of a of work Clarinet be character The instrument actually changes Although it because changed 1 side opened 1 side close to both sides open because open a fingering hold talk for the demonstrated that as well a clarinet actually has a little hole here right at the top of the instrument and that will change both Pictures most character The song shares
I area in a in Seoul The lower register little register much of war 1 miles sound and register And that comes Because I'm getting both The odd and even overtones And the higher registers and in the lower register I get only the O'Reilly orderly The the soul of this that to perhaps finish
Potenzialausgleich
Direkte Messung
Gagat
Weizenbier-Brauerei J. Bayer
Tonfrequenz
Energieniveau
Kaliber <Walzwerk>
Chirp
Leistungssteuerung
Spiralbohrer
Schwellenspannung
Ozonschicht
Elementarteilchenphysik
Starkregen
GIRL <Weltraumteleskop>
Schalldruck
Schall
Relativistische Mechanik
Kaltumformen
Basis <Elektrotechnik>
Nivelliergerät
Nahfeldkommunikation
Rauschsignal
Energielücke
Werkzeug
Jahr
Source <Elektronik>
Absolute Datierung
Intensitätsverteilung
Unterwasserfahrzeug
Schall
Umlaufbahn
Nivelliergerät
Fahrzeug
Besprechung/Interview
Leitungstheorie
Übungsmunition
DVD-Player
DVD-Player
Pager
Intensitätsverteilung
Multiplizität
Tischler
Schalldruck
Erder
Temperatur
Intervall
Erwärmung <Meteorologie>
Konfektionsgröße
Optisches Spektrum
Energieniveau
Webmaschine
Satz <Drucktechnik>
Schallmauer
Regelstrecke
Maßstab <Messtechnik>
Prozessleittechnik
Hörschwelle
Passfeder
Druck
Amplitude
Thermodynamische Temperaturskala
Längenmessung
Nivelliergerät
Canadair CL-44
Urkilogramm
Übungsmunition
Greiffinger
Farbcodierung
Werkzeug
Regentropfen
Reflexionskoeffizient
Atmosphäre
Druckfeld
Jahr
Rauschunterdrückung
Intensitätsverteilung
Betazerfall
Anstellwinkel
Düsenflugzeug
Wärmequelle
Chromatischer Abbildungsfehler
Maßstab <Messtechnik>
Oktober
Tonfrequenz
Auslenkung
Chirp
Schallintensität
Nanometerbereich
Ruhestrom
Fuß <Maßeinheit>
Schalldruck
Schall
Gasdichte
Relativistische Mechanik
Tonfrequenz
Knicklenkung
Eisenbahnbetrieb
Lenkflugkörper
Arche
Band <Textilien>
Heft
Hubraum
Ersatzteil
Luftdruck
Tischler
Unterschallgeschwindigkeit
Chromatischer Abbildungsfehler
Gewicht
Greiffinger
Temperatur
Stringtheorie
Konfektionsgröße
Oktober
Besprechung/Interview
Tonfrequenz
Wellenlänge
Cocktailparty-Effekt
Kaliber <Walzwerk>
Schwingungsmembran
ASTRA <Satellit>
Oberschwingung
Maßstab <Messtechnik>
Astronaut
Steven <Schiffbau>
Ton <Akustik>
Randspannung
Wellenlänge
Massenresonanz
Metallschicht
Juni
Messgerät
Band <Textilien>
Säge
Grundfrequenz
Ruderboot
Mikrowelle
Modellbauer
Tonhöhe
Mechanikerin
Konfektionsgröße
Kaliber <Walzwerk>
Regelstrecke
Prozessleittechnik
Fahrgeschwindigkeit
Schiene
Randspannung
Druckgradient
Wellenlänge
Nivelliergerät
Hydraulikleitung
Standardzelle
Sonnenenergie
Drachenpunkt
Messgerät
Übertragungsverhalten
Übungsmunition
Werkzeug
Atmosphäre
Druckfeld
Direkte Messung
Karton
Fernsehempfänger
Lunker
Eis
Stringtheorie
Tonfrequenz
Wellenlänge
Räderuhr
Auslenkung
Nanometerbereich
Öffentliches Verkehrsmittel
Astronaut
Elementarteilchenphysik
Chandrasekhar-Grenze
Schall
Tonfrequenz
Grundfrequenz
Oberschwingung
Stringtheorie
Minute
Druckkraft
Thermalisierung
Elektrogitarre
Elektromigration
Kurzschlussstrom
Grundfrequenz
Schraubstock
Innere Reibung
Mikrowelle
Wind
Gummifeder
Gammabestrahlung
Mechanikerin
Röhrenverstärker
Holzfaserplatte
Wellenlänge
Feldstärke
Summer
Oberschwingung
Windpark
Auslenkung
Drachenpunkt
Messgerät
Übungsmunition
Werkzeug
Angeregtes Atom
Grundfrequenz
Atmosphäre
Backenbremse
Druckfeld
Schalttafel
Mikrowelle
Öffentliches Verkehrsmittel
Elementarteilchenphysik
Regler
Locher
Tonfrequenz
Auslenkung
Kaliber <Walzwerk>
Satz <Drucktechnik>
Reed-Relais
Förderleistung
Abformung
Angeregtes Atom
Holz
Prozessleittechnik
Blende <Kleidung>
Biegen
Ton <Akustik>
Energielücke
Klangeffekt
Stunde
Wellenlänge
Kaltumformen
Kraft-Wärme-Kopplung
Waffentechnik
Rollsteig
Schrott
Rauschzahl
Messgerät
Hall-Effekt
Übungsmunition
Greiffinger
TEM-Welle
Reed-Relais
Mitlauffilter
Schwarzes Loch
Grundfrequenz
Paillette
Atmosphäre
Flüssiger Brennstoff
Druckfeld
Jahr
Zylinderkopf
Wind
Gammabestrahlung
Direkte Messung
Luftdruck
Kosmische Strahlung
Quantenfluktuation
Spanwerkzeug
Niederfrequenz
Blechdose
Amplitude
Optisches Spektrum
Chirp
Nanometerbereich
Optisches Spektrum
Woche
ASTRA <Satellit>
Schall
DVD-Player
Oberschwingung
Prozessleittechnik
Fahrgeschwindigkeit
Ton <Akustik>
Drehmasse
Schall
Kaltumformen
Rauschsignal
Tonfrequenz
Grundfrequenz
Kraft-Wärme-Kopplung
Oberschwingung
Metallschicht
Eisenbahnbetrieb
Proof <Graphische Technik>
Messgerät
Übungsmunition
Band <Textilien>
Elektronische Medien
Greiffinger
TEM-Welle
Reed-Relais
Werkzeug
Angeregtes Atom
Anhänger
Hohlwelttheorie
Schwarzes Loch
Grundfrequenz
Atmosphäre
Edelsteinindustrie
Mikrowelle
Wind
Buntheit
Registrierkasse

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Titel Basic Physics III Lecture 7
Serientitel Basic Physics III
Teil 7
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 10.5446/12943
Herausgeber University of California Irvine (UCI)
Erscheinungsjahr 2013
Sprache Englisch

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Fachgebiet Physik

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