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f obs = f s 1 v c 1 + v c .

Notice that the signs are different from those of the wavelength equation.

Calculating a doppler shift

Suppose a galaxy is moving away from Earth at a speed 0.825 c . It emits radio waves with a wavelength of
0.525 m. What wavelength would we detect on Earth?


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.


  1. Identify the knowns: u = 0.825 c ; λ s = 0.525 m.
  2. Identify the unknown: λ obs .
  3. Express the answer as an equation:
    λ obs = λ s 1 + v c 1 v c .
  4. Do the calculation:
    λ obs = λ s 1 + v c 1 v c = ( 0.525 m) 1 + 0.825 c c 1 0.825 c c = 1.70 m.


Because the galaxy is moving away from 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. You will see in Particle Physics and Cosmology that detecting redshifted radiation led to present-day understanding of the origin and evolution of the universe.

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Check Your Understanding Suppose a space probe moves away from Earth at a speed 0.350 c . It sends a radio-wave message back to Earth at a frequency of 1.50 GHz. At what frequency is the message received on Earth?

We can substitute the data directly into the equation for relativistic Doppler frequency:
f obs = f s 1 v c 1 + v c = ( 1.50 GHz) 1 0.350 c c 1 + 0.350 c c = 1.04 GHz.

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The relativistic Doppler effect has applications ranging from Doppler radar storm monitoring to providing information on the motion and distance of stars. We describe some of these applications in the exercises.


  • 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 = λ s 1 + v c 1 v c .

    where λ obs is the observed wavelength, λ s is the source wavelength, and v is the relative velocity of the source to the observer.

Conceptual questions

Explain the meaning of the terms “red shift” and “blue shift” as they relate to the relativistic Doppler effect.

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What happens to the relativistic Doppler effect when relative velocity is zero? Is this the expected result?

There is no measured change in wavelength or frequency in this case. The relativistic Doppler effect depends only on the relative velocity of the source and the observer, not any speed relative to a medium for the light waves.

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Is the relativistic Doppler effect consistent with the classical Doppler effect in the respect that λ obs is larger for motion away?

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All galaxies farther away than about 50 × 10 6 ly exhibit a red shift in their emitted light that is proportional to distance, with those farther and farther away having progressively greater red shifts. What does this imply, assuming that the only source of red shift is relative motion?

It shows that the stars are getting more distant from Earth, that the universe is expanding, and doing so at an accelerating rate, with greater velocity for more distant stars.]

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A highway patrol officer uses a device that measures the speed of vehicles by bouncing radar off them and measuring the Doppler shift. The outgoing radar has a frequency of 100 GHz and the returning echo has a frequency 15.0 kHz higher. What is the velocity of the vehicle? Note that there are two Doppler shifts in echoes. Be certain not to round off until the end of the problem, because the effect is small.

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Questions & Answers

can someone explain normalization condition
Priyojit Reply
1 millimeter is How many metres
Darling Reply
1millimeter =0.001metre
The photoelectric effect is the emission of electrons when light shines on a material. 
Chris Reply
What is photoelectric effect
Amit Reply
it gives practical evidence of particke nature of light.
particle nature
photoelectric effect is the phenomenon of emission of electrons from a material(i.e Metal) when it is exposed to sunlight. Emitted electrons are called as photo electrons.
what are the applications of quantum mechanics to medicine?
application of quantum mechanics in medicine: 1) improved disease screening and treatment ; using a relatively new method known as BIO- BARCODE ASSAY we can detect disease-specific clues in our blood using gold nanoparticles. 2) in Genomic medicine 3) in protein folding 4) in radio theraphy(MRI)
Quantam physics ki basic concepts?
Laxmikanta Reply
why does not electron exits in nucleaus
Kabbo Reply
electrons have negative
Proton and meltdown has greater mass than electron. So it naturally electron will move around nucleus such as gases surrounded earth
.......proton and neutron....
excuse me yash what negative
coz, electron contained minus ion
negative sign rika shrestha ji
electron is the smallest negetive charge...An anaion i.e., negetive ion contains extra electrons. How ever an atom is neutral so it must contains proton and electron
yes yash ji
yes friends
koantam theory
yes prema
quantum theory tells us that both light and matter consists of tiny particles which have wave like propertise associated with them.
proton and nutron nuclear power is best than proton and electron kulamb force
what is de-broglie wave length?
plot a graph of MP against tan ( Angle/2) and determine the slope of the graph and find the error in it.
Ime Reply
expression for photon as wave
Are beta particle and eletron are same?
Amalesh Reply
how can you confirm?
If they are same then why they named differently?
because beta particles give the information that the electron is ejected from the nucleus with very high energy
what is meant by Z in nuclear physic
Shubhu Reply
atomic n.o
no of atoms present in nucleus
miss sanjana your question is wrong...question should be no of nucleus present in an atom...and answer is 1...
Owaise is right
Z = number of protons in a nucleus of an atom
Note on spherical mirrors
Shamanth Reply
what is Draic equation? with explanation
M.D Reply
trpathy Reply
it's a subject
it's a branch in science which deals with the properties,uses and composition of matter
what is a Higgs Boson please?
god particles is know as higgs boson, when two proton are reacted than a particles came out which is used to make a bond between than materials
bro little abit getting confuse if i am wrong than please clarify me
the law of refraction of direct current lines at the boundary between two conducting media of

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Source:  OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4
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