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Theme C — Wave Behaviour

C.5.2 The Doppler Effect of Light — IB Physics HL Revision Notes & Topical Questions

5 min read 8 parts Lesson 35 of 37 1 quiz

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Curriculum Equation Key Wave Speed & Doppler Effect FormulasFast Exam Solution
v = f × λ | f_obs = f × (v ± v_o) / (v ∓ v_s) | T = 1 / f
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Lesson summary

C.5.2 The Doppler Effect of Light — IB PHYSICS SL notes: Use Δλ/λ ≈ Δf/f ≈ v/c to find the radial speed of a light source from its shift in wavelength or frequency.Medium — light needs none, so there is no preferred frameDependence — the shift depends only on the relative velocit…

  • Meaning of the words
  • Relative speed
  • Redshift z
  • What the symbols mean
  • Rearranged
  • Fingerprint

Part 1 of 6Light and relative motion

Medium
  • Medium light needs none, so there is no preferred frame
Dependence
  • Dependence the shift depends only on the relative velocity of source and observer along the line joining them
    • (the radial velocity)
Redshift
  • Redshift a source moving away has an observed wavelength longer than the emitted one
Blueshift
  • Blueshift a source moving towards the observer has an observed wavelength shorter than the emitted one
Meaning of the words
  • Meaning of the words they describe the direction of the shift along the spectrum, not necessarily the colours seen
  • The whole spectrum moves, not just red colours.

Part 2 of 6The equation for low speeds

Equation
  • Δλ/λ ≈ Δf/f ≈ v/c, valid only when v ≪ c
Symbols
  • Δλ = λobserved − λemitted.
  • λ is the wavelength emitted by the source, measured in its own frame such as in the laboratory.
  • Δf is the change in frequency in magnitude.
  • v is the relative speed along the line of sight and c = 3.00 × 108 m s−1.
Relative speed
  • Relative speed v = vs − vo, and for a stationary observer v equals the speed of the source
Units
  • Units the shift has no units because the fractions have matching units, so nm need not be converted to m
Accuracy
  • Accuracy the approximation is within about 1% for speeds up to a few per cent of c
Redshift z
  • Redshift z z = Δλ/λ,
  • so v ≈ cz when z is small
    What the symbols mean: Δλ = change in wavelength · λ = emitted wavelength · v = speed of the source along the line of sight · c = 3.00 × 108 m s−1
Rearranged
  • Rearranged v = cΔλ/λ

Part 3 of 6Using spectra

Fingerprint
  • Fingerprint atoms emit or absorb light at precise wavelengths characteristic of each element
  • Hydrogen gives the Balmer lines, one at 656.3 nm.
Star spectra
  • Star spectra a star's atmosphere gives absorption lines of its elements
Shift
  • Shift when the star moves relative to us all the lines shift by the same fractional amount
Method
  • Method compare the observed wavelength of an identified line with its laboratory value to find Δλ, then v
Direction
  • Direction lines shifted to the red end of the spectrum mean the source moves away from Earth
Limit
  • Limit only the component of velocity along the line of sight is found
  • Motion across the sky is not detected, so the true speed is at least the measured value.
Precision
  • Precision very small shifts are measured with long exposures and gratings of high resolving power

Part 4 of 6Applications in astronomy

Applications in astronomy
Binary stars
  • Binary stars the lines of two orbiting stars shift periodically, redshifting as a star recedes and blueshifting as it approaches
  • The period of the cycle is the orbital period.
Exoplanets
  • Exoplanets a star wobbles as a planet tugs on it, causing tiny periodic line shifts of metres per second
  • This reveals planets that cannot be seen directly.
Rotation
  • Rotation light from one edge of a rotating star or galaxy is blueshifted and from the other edge redshifted
  • The lines widen and the rotation speed can be found from the shift.
  • A 0.1 nm shift of a visible hydrogen line corresponds to about 46 km s−1.
Monitoring over time
  • Monitoring over time a line moving back and forth shows a small orbit
  • The period and speed give the orbital radius and the mass of an unseen companion.
Expansion of the universe
  • Expansion of the universe the redshift of distant galaxies is covered in C.5.3

Part 5 of 6Cautions

Speeds near c
  • Speeds near c the low-speed formula fails and relativistic Doppler formulas are needed
Other redshifts
  • Other redshifts gravitational redshift of light leaving a strong field is different, and cosmological redshift comes from the stretching of space
  • For IB purposes the cosmological redshift uses the same formula for z.
Sound versus light
  • Sound versus light the sound formulas differ in form because sound has a medium
Photon energy
  • Photon energy a redshifted photon has less energy, E = hf
    What the symbols mean: E = energy of one photon (J) · h = Planck constant (6.63 × 10−34 J s) · f = frequency (Hz)

Part 6 of 6More from the specification

1Doppler Effect for Electromagnetic Waves
  • The shift in observed frequency and wavelength of radiation emitted by a source moving relative to the observer in an inertial frame of reference.
2Galactic Redshift
  • The observed stretching of spectral absorption lines toward longer wavelengths for distant celestial objects, indicating that galaxies are moving away from Earth.
3Cosmological Expansion
  • Systematic galactic redshift means the fabric of spacetime itself is expanding, modeled at non-relativistic speeds by the fractional wavelength shift Delta lambda / lambda_0 = v / c.
4Sound Waves vs Electromagnetic Doppler Shift
  • While sound from a moving siren requires a physical acoustic medium, electromagnetic waves travel through vacuum at the invariant speed of light.
5Electromagnetic wave
  • Transverse wave that transfers energy from a source to an absorber
6Galactic redshift
  • Shift of galaxy spectral lines to longer wavelength due to recession.

Key terms

TermMeaning
RedshiftIncrease in observed wavelength due to recession.
BlueshiftDecrease in observed wavelength due to approach.
Radial velocityVelocity component along the line of sight.
Spectral lineCharacteristic wavelength emitted or absorbed by an element.
Redshift zFractional change in wavelength, z = Δλ/λ.

Avoid these mistakes

1
Using the formula for speeds close to c.
2
Thinking a redshift is a change to red colour only — the whole spectrum moves.
3
Forgetting that only radial motion contributes.
4
Mixing the sign — redshift means receding.
5
Using the observed wavelength in the denominator without noting that the formula is only approximate.

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Cambridge 9702 & Edexcel Physics Mark Scheme Points

Doppler Shift & Galactic Red-shift Criteria

Key Equation: Δλ / λ ≈ Δf / f ≈ v / c

  • Red-shift: Fractional increase in observed wavelength from receding galaxies.
  • Hubble's Law: v = H0d (Universe age ≈ 1 / H0).
  • Evidence for Big Bang: Cosmological red-shift + CMBR at 2.7K.