Slide show Notes_06: Relativistic Doppler Effect .


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Slide show Notes_06.ppt: Relativistic Doppler Effect . You have learned about the Doppler Effect (DE) in Physics 212, right? Perhaps even earlier, at high school, or from your own reading – because DE plays such an important role in our life (e.g., police uses DE to catch speed
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Slide 1

Slide indicate Notes_06.ppt: Relativistic Doppler Effect You have found out about the Doppler Effect (DE) in Physics 212, correct? Maybe considerably prior, at secondary school, or from your own perusing – on the grounds that DE assumes such a vital part in our life (e.g., police utilizes DE to catch speed constrain violators!) and in science (e.g., from investigations of the supposed "Doppler move" stargazers have found out about the extending Universe). The essential system of DE for sound waves (i.e., at which the DE material in Ph212 principally engaged) is not quite the same as that for light waves: in the DE for sound waves the medium, (for example, air, water) assumes a pivotal part – however in the light proliferation no medium is included! Likewise, which is entirely self-evident, every single relativistic impact (time expansion, length withdrawal) are unimportantly little in the DE for sound and other mechanical waves. In any case, only to refresh your memory, it is worth regardless a brief review of the DE for sound waves.

Slide 2

Let\'s revive our memory: DE for sound waves Let\'s begin with a fairly improved model. The transmitter (amplifier) emanates a sound wave, and at some separation from it There is a beneficiary (e.g., a human ear, in the photo beneath symbolized by the question-mark-like shape). We can think about the accepting procedure that every time a sound wave "peak" achieves the recipient, it creates a PING! Some such "pings" heard in a brief moment give us the impression of a nonstop stable (the genuine mecha-nism of hearing is most likely more confused, yet the essential material science in our model is OK (really, to analyze the fundamental standards of DE, rather than considering a consistent wave, one can think about a sound flag as a grouping of short solid signs: ping!- ping!- ping!- ping-ping!

Slide 3

Well, here is an indistinguishable liveliness from in the previous slide, yet backed off – take note of that every PING! happens precisely right when a "peak" (i.e., a greatest) comes to the "ear".

Slide 4

Now, consider two spectators, of which one is stationary, and alternate moves towards the sound source with consistent speed: Note that the moving onlooker enrolls more Pings! per time unit than the stationary one – it implies that she/he enlists a higher recurrence. Address: how might the recurrence change if the second spectator moved far from the sound source? Yes, obviously – then the recurrence would be lower,

Slide 5

The same as some time recently, yet backed off a bit: note that in both cases the PING! Shows up exactly right now a back to back greatest achieves the ear:

Slide 6

Now, we should discuss the relativistic Doppler impact. Presently, the flag transmitted by one spectator, and got by another, is a light wave. It has a signifant effect contrasted with the circumstance in Doppler impact with sound waves: there is no medium, and the speed of the wave (i.e., of light) is the same for both eyewitnesses. Furthermore, the "transmitter" and "beneficiary" move in respect to each other with such a speed, to the point that relativistic impacts must be considered. We will consider the accompanying circumstance: the "transmitter" is in the casing O that moves away with speed - u (which means: to one side) from the edge O\' in which the "beneficiary" found. At some minute the "transmitter" begins to communicate a light wave. On the following slide, you will see an activity. The position of O right now it begins transmitting will be shown by a marker, and another marker will demonstrate the position of O right now The light flag achieves O\'.

Slide 7

The movement is rehashed a few times, and after that it stops: On the following slide, we will play out a few estimations.

Slide 8

A sum of N waves conveyed from O – the time that elap ed between the start of transmission and the minute the wave-front achieved the spectator O\' , measured in the O\' outline. For the O\' eyewitness, the N waves conveyed from the O source are extended over the separation

Slide 9

Hence, the wavelength λ " as indicated by the O\' onlooker is: Denote the time enlisted in the O outline between the start of transmission and the minute the wave-front achieved O\' as Δ t 0 , And the recurrence of the flag for the O spectator as ν . The recurrence can be considered as the quantity of waves conveyed in a period unit. In this way, the aggregate number of waves transmitted is By consolidating the two conditions, we acquire:

Slide 10

The general connection between the wavelength and recurrence of a light wave is: wavelength = (speed of light)/(recurrence). In this manner, the wavelength and the recurrence the O\' onlooker registers are connected as: After likening this with the outcome for similar wavelength at the base of the first slide, and some basic polynomial math, we get: Now, we can utilize the time enlargement recipe:

Slide 12

Let\'s contrast the relativistic DE and the traditional DE for sound waves: The general recipe for the Doppler recurrence move of sound waves is: If we consider a closely resembling circumstance as some time recently, then just the source moves: We utilized:

Slide 13

Comparison of relativistic and established DE, proceeded with: Now how about we utilize the condition we have determined for the relativistic recurrence move. How about we accept that the source speed u is little contrasted and the speed of light; then, we can utilize an indistinguishable estimate from we have utilized as a part of the first slide: It is similar recipe that we acquired a minute prior for sound waves. Be that as it may, for source or spectator speeds tantamount with the speed of light one can no longer utilize an indistinguishable recipe from for sound waves. However, are there any such circumstances that we can watch? The answer is YES! Because of the development of Universe, far off cosmic systems are moving far from our world with such speeds that we need to utilize the correct equation.

Slide 14

A vital thing to recall: The Doppler move in the recurrence of light waves touching base from inaccessible cosmic systems is one of the primary wellsprings of our insight into the Universe. The light touching base from far off universes is moved toward lower frequencies. This is called "the blushing of worlds". How would we realize that the recurrence is lower? Indeed, all stars radiate certain trademark "ghastly lines", the recurrence of which is outstanding. One of such lines is "the blue line of hydrogen", with wavelength λ = 434 nm . Assume that in the light from an inaccessible cosmic system similar line has a wavelength of λ \'= 600 nm – such light is do not blue anymore, however red (along these lines, the expression "blushing"). Address: what is the "subsiding speed" u of that universe? Speedy test: Find the % mistake in the estimation of u acquired utilizing the established equation for the Doppler recurrence move.

Slide 15

The astonishing TWIN PARADOX There are two twins, Amelia and Casper. Casper remains focused Amelia takes off in a spaceship and goes to a removed star...

Slide 16

Twin Paradox, proceeded. ...while for Amelia, because of the time expansion, the timetable progressed slower, And she is still youthful... Casper is extremely glad when she returns... Be that as it may, he is presently an old man... Is this story predictable with the relativity hypothesis?

Slide 17

Twin Paradox, proceeded with (2). Be that as it may, somebody may say: I see the entire thing in an unexpected way. The relativity hypothesis says that all frameworks are comparable, correct? Thus, from Amelia\'s viepoint, it is Casper who brings off with the whole planet. ... Accordingly, it is the Casper\'s clock that will "tick" slower than Amelia\'s clock, and it is Casper will\'s identity more youthful when they meet once more!

Slide 18

Twin Paradox, proceeded with ( 3 ). Who is correct?! I recommend that we resolve this difficulty by DEMOCRATIC MEANS Let\'s vote! Who believes that Casper will be more seasoned, raise your hand! Also, now, who imagines that Amelia will be more seasoned, raise your hand!

Slide 19

Twin Paradox, proceeded with (4). The issue is not paltry! It evoked a warmed examination not long after the distribution of Einstein\'s 1905 paper, in which it was said surprisingly. Than, there was another energetic exchange in the 1950s – most likely, on the grounds that it was a time of America\'s extraordinary interest with SF writing. Simply following a couple of years of civil argument, and after the distribution of around 40 articles on that theme in different logical diaries, somebody got the right thought how to take care of the issue – in particular by utilizing THE DOPPLER EFFECT keeping in mind the end goal to clarify how the Doppler Effect can, "we should do the numbers". Assume that Amelia\'s travel goal is a star 12 light-years from Earth (i.e., light from this star needs to travel 12 years until it achieves Earth). Next, assume that Amelia\'s shuttle goes with a speed of 0.6 c . In this way, it sets aside 20 years Earth time for Amelia to get to the star, and 20 years to head out back to Earth. Be that as it may, because of time expansion , in Amelia\'s edge just will pass on her way to the star, and an additional 16 years on her way back to Earth

Slide 20

Twin Paradox, proceeded with ( 5 ). Assume that Amelia takes off precisely on a day that is hers and Casper\'s birthday. Furthermore, assume that before Amelia\'s takeoff the two kin settle on the accompanying choice: on his each next birthday (Earth time) Casper will send Amelia a light flag. An on each birthday of hers – rocket time – she will send Casper a comparative light flag. Well , so the recurrence of the light flags Casper conveys is: Using the recipe for relativistic recurrence move, we discover the recurrence ν " with which Amelia gets Casper\'s signs: During the 16-year flight to the star, Amelia will consequently get 8 Casper\'s light flags

Slide 21

Twin Paradox, proceeded with ( 6 ). In any case, on her way back to Earth, Amelia\'s rocket speed is It makes a distinction! Since now the fr

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