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Doppler shift

Although the speed of light does not change with relative velocity, the frequencies and wavelengths of light do. First discussed for sound waves, a Doppler shift occurs in any wave when there is relative motion between source and observer.

Relativistic doppler effects

The observed wavelength of electromagnetic radiation is longer (called a red shift) than that emitted by the source when the source moves away from the observer and shorter (called a blue shift) when the source moves towards the observer.

obs s 1 + u c 1 u c . size 12{λ rSub { size 8{"obs"} } ital "=λ" rSub { size 8{s} } sqrt { { {1+ { {u} over {c} } } over {1 - { {u} over {c} } } } } } {}

In the Doppler equation, λ obs size 12{λ rSub { size 8{"obs"} } } {} is the observed wavelength, λ s size 12{λ rSub { size 8{s} } } {} is the source wavelength, and u size 12{u} {} is the relative velocity of the source to the observer. The velocity u size 12{u} {} is positive for motion away from an observer and negative for motion toward an observer. In terms of source frequency and observed frequency, this equation can be written

f obs =f s 1 u c 1 + u c . size 12{f rSub { size 8{"obs"} } ital "=f" rSub { size 8{s} } sqrt { { {1 - { {u} over {c} } } over {1+ { {u} over {c} } } } } } {}

Notice that the – and + signs are different than in the wavelength equation.

Career connection: astronomer

If you are interested in a career that requires a knowledge of special relativity, there’s probably no better connection than astronomy. Astronomers must take into account relativistic effects when they calculate distances, times, and speeds of black holes, galaxies, quasars, and all other astronomical objects. To have a career in astronomy, you need at least an undergraduate degree in either physics or astronomy, but a Master’s or doctoral degree is often required. You also need a good background in high-level mathematics.

Calculating a doppler shift: radio waves from a receding galaxy

Suppose a galaxy is moving away from the Earth at a speed 0.825 c . It emits radio waves with a wavelength of 0 . 525 m size 12{0 "." "525"" m"} {} . What wavelength would we detect on the Earth?

Strategy

Because the galaxy is moving at a relativistic speed, we must determine the Doppler shift of the radio waves using the relativistic Doppler shift instead of the classical Doppler shift.

Solution

  1. Identify the knowns. u= 0 . 825 c size 12{ ital "u="0 "." "825"c} {} ; λ s = 0 . 525 m size 12{λ rSub { size 8{s} } =0 "." "525"`m} {}
  2. Identify the unknown. λ obs size 12{λ rSub { size 8{"obs"} } } {}
  3. Choose the appropriate equation. λ obs s 1 + u c 1 u c size 12{λ rSub { size 8{"obs"} } ital "=λ" rSub { size 8{s} } sqrt { { {1+ { {u} over {c} } } over {1 - { {u} over {c} } } } } } {}
  4. Plug the knowns into the equation.
    λ obs = λ s 1 + u c 1 u c = ( 0.525 m ) 1 + 0 . 825 c c 1 0 . 825 c c = 1.70 m.

Discussion

Because the galaxy is moving away from the Earth, we expect the wavelengths of radiation it emits to be redshifted. The wavelength we calculated is 1.70 m, which is redshifted from the original wavelength of 0.525 m.

The relativistic Doppler shift is easy to observe. This equation has everyday applications ranging from Doppler-shifted radar velocity measurements of transportation to Doppler-radar storm monitoring. In astronomical observations, the relativistic Doppler shift provides velocity information such as the motion and distance of stars.

Suppose a space probe moves away from the Earth at a speed 0 . 350 c size 12{0 "." "350"c} {} . It sends a radio wave message back to the Earth at a frequency of 1.50 GHz. At what frequency is the message received on the Earth?

Answer

f obs =f s 1 u c 1 + u c = ( 1 . 50 GHz ) 1 0 . 350 c c 1 + 0 . 350 c c = 1 . 04 GHz size 12{f rSub { size 8{"obs"} } ital "=f" rSub { size 8{s} } sqrt { { {1 - { {u} over {c} } } over {1+ { {u} over {c} } } } } = \( 1 "." "50 GHz" \) sqrt { { {1 - { {0 "." "350" ital " c"} over {c} } } over {1+ { {0 "." "350" ital " c"} over {c} } } } } =1 "." "04 GHz"} {}

Section summary

  • With classical velocity addition, velocities add like regular numbers in one-dimensional motion: u=v+u size 12{ ital "u=v+u" rSup { size 8{'} } } {} , where v size 12{v} {} is the velocity between two observers, u size 12{u} {} is the velocity of an object relative to one observer, and u size 12{u rSup { size 8{'} } } {} is the velocity relative to the other observer.
  • Velocities cannot add to be greater than the speed of light. Relativistic velocity addition describes the velocities of an object moving at a relativistic speed:
    u= v+u 1 + v u c 2
  • An observer of electromagnetic radiation sees relativistic Doppler effects    if the source of the radiation is moving relative to the observer. The wavelength of the radiation is longer (called a red shift) than that emitted by the source when the source moves away from the observer and shorter (called a blue shift) when the source moves toward the observer. The shifted wavelength is described by the equation
    λ obs s 1 + u c 1 u c size 12{λ rSub { size 8{"obs"} } ital "=λ" rSub { size 8{s} } sqrt { { {1+ { {u} over {c} } } over {1 - { {u} over {c} } } } } } {}
    λ obs size 12{λ rSub { size 8{"obs"} } } {} is the observed wavelength, λ s size 12{λ rSub { size 8{s} } } {} is the source wavelength, and u size 12{u} {} is the relative velocity of the source to the observer.

Questions & Answers

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biomolecules are e building blocks of every organics and inorganic materials.
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research.net
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Introduction about quantum dots in nanotechnology
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nano basically means 10^(-9). nanometer is a unit to measure length.
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there is no specific books for beginners but there is book called principle of nanotechnology
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s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
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Mostly, they use nano carbon for electronics and for materials to be strengthened.
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carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
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s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
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of graphene you mean?
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or in general
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Graphene has a hexagonal structure
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Source:  OpenStax, Physics 101. OpenStax CNX. Jan 07, 2013 Download for free at http://legacy.cnx.org/content/col11479/1.1
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