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IB DP Physics · Theme C Wave behaviour · C.5 · ~5 min read

C.5 Doppler effect

The Doppler effect for sound and light, wavefront diagrams for a moving source, redshift and blueshift of spectral lines as evidence for moving stars and galaxies, and (HL) the moving-source and moving-observer equations for sound.

Doppler effectWavefront diagramsRedshift & blueshiftΔf/f ≈ v/cMoving source (HL)Moving observer (HL)
RSby Riyaz Sir
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No tag = SL and HLHL ONLY HL students onlyDATA BOOKLET given in the examM1A1 how marks are awardedhighlight = comes up again and againTest yourself at the end

In 30 seconds

  • The Doppler effect is the change in observed frequency and wavelength when the source and observer move relative to each other.
  • Approaching: higher frequency, shorter wavelength. Moving apart: lower frequency, longer wavelength.
  • For light (v ≪ c): Δf/f = Δλ/λ ≈ v/c. Spectral lines from receding galaxies are redshifted, the key evidence for the expanding universe.
  • HL: for sound, f′ = f v/(v ± us) for a moving source and f′ = f(v ± uo)/v for a moving observer.

By the end you can

  • Describe the Doppler effect for sound and EM waves with wavefront diagrams.
  • Use Δf/f = Δλ/λ ≈ v/c for light.
  • Explain redshift and blueshift as evidence for the motion of stars and galaxies.
  • Use the Doppler equations for a moving source and a moving observer of sound. HL

1What the Doppler effect is

usin front:λ shorter,f higherbehind:λ longer,f lowerThe source moves between emitting wavefronts, so they bunch up ahead of it.
Each circle was emitted from where the source was at that moment.
  • Why: the wave speed through the medium does not change, but a moving source emits each wavefront from a new position, so the wavefronts are closer together ahead of it. A moving observer meets wavefronts more often (or less often).
  • Everyday examples: the falling pitch of a passing siren or racing car; police radar; ultrasound measuring blood flow.

2Light: redshift and blueshift

Δff = Δλλ ≈ vc DATA BOOKLET
for EM waves when v is much less than c; v is the relative speed
labgalaxyLines shifted to longer wavelength: the galaxy is moving away (redshift).
The pattern of lines is the same, just shifted. That proves it is the same element, moving.
Worked example

The hydrogen line at 656.3 nm is observed at 662.0 nm in a galaxy's spectrum. Find the galaxy's speed and direction.

  1. Δλ = 662.0 − 656.3 = 5.7 nm A1
  2. v = cΔλ/λ = 3.00 × 108 × 5.7/656.3 M1
  3. = 2.6 × 106 m s−1, moving away (redshift) A1
  • Evidence from astronomy: distant galaxies are redshifted, and more distant ones more strongly: the universe is expanding. Binary stars show lines that shift back and forth as the stars orbit each other.
Common mistakeMixing up Δλ and λ. Δλ is the change (observed − emitted); λ is the emitted (lab) wavelength.

3Sound: the Doppler equations HL

f′ = fvv ± us DATA BOOKLET
moving source: − when approaching, + when receding
f′ = fv ± uov DATA BOOKLET
moving observer: + when approaching, − when receding
Worked example

A siren of 500 Hz moves at 30 m s−1 (v = 340 m s−1). Find the frequency heard as it approaches and as it moves away.

  1. approaching: f′ = 500 × 340/(340 − 30) = 548 Hz M1A1
  2. receding: f′ = 500 × 340/(340 + 30) = 460 Hz A1
Worked example

A cyclist rides at 20 m s−1 towards a stationary 500 Hz source. What frequency does she hear?

  1. f′ = f(v + uo)/v = 500 × 360/340 M1
  2. = 529 Hz A1
Memory trickSign check: approaching must always give a higher frequency. Pick the sign that does that, and you never need to memorise the table.
Exam tipIn a "sketch how the frequency heard changes" question for a passing source: a constant high frequency while approaching, a sudden drop as it passes, then a constant low frequency (if the source moves in a straight line through you).
Linking questionRedshift data feed into E.5 (stars and the universe). The relativistic Doppler effect and time dilation in A.5 are linked, but only the v ≪ c approximation is needed here.
Idea for your IA / explorationRecord a moving sound source (a buzzer on a rotating arm or a passing car) with a phone app, measure the frequency shift and deduce the speed, then compare with a direct measurement.

Test yourself — cover the answers first

Quick check

  1. Does the speed of sound change when the source moves?
  2. What is redshift?
  3. Why do spectral lines give strong evidence for galaxy motion?
  4. A star's line shifts to a shorter wavelength. Is it approaching or receding?
  5. HL Which gives the bigger frequency change: source or observer moving at the same speed towards each other?

Exam-style

  1. A star's spectral line at 500.0 nm (lab) is observed at 499.5 nm. Find its speed.
  2. HL A train horn is heard at 520 Hz as the train approaches and 480 Hz as it leaves (v = 340 m s−1). Find the train's speed.
Show answers
  1. No: frequency and wavelength change, not the wave speed in the medium.
  2. an increase in the observed wavelength because the source is moving away
  3. the same pattern of lines is shifted, so it is the same element moving
  4. approaching (blueshift)
  5. the moving source (slightly larger)
  6. Δλ = −0.5 nm
    v = c × 0.5/500
    = 3.0 × 105 m s−1 towards us
  7. 520(340 − u) = 480(340 + u)
    176 800 − 520u = 163 200 + 480u
    u = 13 600/1000 = 13.6 m s−1
Practise this chapter
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Next chapterD.1 Gravitational fields →
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Independent notes written by Riyaz Sir. Not produced, endorsed or approved by the International Baccalaureate Organization. Syllabus codes refer to the IB DP subject guides.