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IB Physics HL/Notes/C.5 Doppler effect

IB Physics HLC.5 Doppler effectNotes

Model Doppler effect

The source emits waves at its own emitted frequency, but relative motion changes the spacing of wavefronts reaching the observer. Approaching motion makes successive wavefronts arrive closer together in time, so the detected frequency is higher. Receding motion makes them arrive farther apart in time, so the detected frequency is lower.

The Doppler effect is the change in observed frequency or wavelength of a wave due to relative motion between source and observer.
When source and observer move toward each other, wavefronts are compressed and observed frequency is higher.
When source and observer move away from each other, wavefronts are stretched and observed frequency is lower.
For a given wave speed, higher observed frequency corresponds to shorter observed wavelength, and lower observed frequency corresponds to longer observed wavelength.
The Doppler effect applies to sound waves and electromagnetic waves, though the formula treatment differs.

Choose the observed frequency change from the relative motion.

Decision
The source and observer are moving toward each other.
The source and observer are moving away from each other.
There is no relative motion along the line between source and observer.

A sound source moves towards a stationary observer and then passes the observer. Describe the change in observed frequency before and after it passes.

Saying the emitted frequency changes instead of the observed frequency changing due to relative motion.

A sound source moves towards a stationary observer and then passes the observer. Describe the change in observed frequency before and after it passes.

Choose

Model Doppler wavefront diagrams

A Doppler wavefront diagram is a spacing map. Each wavefront was emitted at a different time, so a moving source changes where the centres of the circles are. Ahead of the source, wavefronts bunch up and the observer receives more wavefronts per second. Behind the source, they are spread out and the observer receives fewer wavefronts per second.

In a moving-source Doppler diagram, wavefronts are closer together in the direction of source motion.
Closer wavefront spacing means shorter observed wavelength and higher observed frequency.
Wavefronts are farther apart behind a moving source, giving longer observed wavelength and lower observed frequency.
For electromagnetic waves, shorter observed wavelength corresponds to blue shift and longer observed wavelength corresponds to red shift.
The sign of the shift depends on relative motion along the line between source and observer.

Label the Doppler wavefront diagram for a source moving to the right.

Label
Labels
5

A diagram shows wavefronts closer together in front of a moving source and farther apart behind it. Explain what an observer in each position detects.

Saying only “the waves are closer” without translating spacing into wavelength and observed frequency.

A diagram shows wavefronts closer together in front of a moving source and farther apart behind it. Explain what an observer in each position detects.

Choose

Model Light Doppler approximation

The light Doppler approximation is a small-shift rule. Measure how far the observed wavelength has moved from its rest value, divide by the rest wavelength, and multiply by c to estimate radial speed. Red shift means the observed wavelength is longer, so the source is moving away. Blue shift means the observed wavelength is shorter, so the source is moving towards the observer.

For electromagnetic waves at speeds much smaller than c, the fractional wavelength shift is z = Δλ/λ0 ≈ v/c for radial motion.
Δλ = λ_obs - λ0, where λ0 is the rest or laboratory wavelength.
Positive Δλ is red shift: wavelength increases, frequency decreases, and the source is receding.
Negative Δλ is blue shift: wavelength decreases, frequency increases, and the source is approaching.
The fractional magnitudes of wavelength and frequency shifts are approximately equal at low speed, but their signs are opposite.
Use c = 3.00 × 10^8 m s^-1 for electromagnetic waves in vacuum.

Build the low-speed light Doppler approximation using observed and rest wavelength.

Formula
Target formula z = (lambda_obs - lambda_0) / lambda_0 ≈ v / c
z
redshift or fractional wavelength shift
lambda_obs
observed wavelength of the spectral line
m
lambda_0
rest or laboratory wavelength of the spectral line
m
v
radial speed of source relative to observer
m s^-1
c
speed of light in vacuum
m s^-1
1Find the wavelength shift from observed and rest wavelengths.Delta lambda = lambda_obs - lambda_0
2Divide by the rest wavelength.z = Delta lambda / lambda_0
3Use the low-speed approximation.z ≈ v / c, so v ≈ zc
4Interpret the sign from wavelength.positive z -> red shift -> receding; negative z -> blue shift -> approaching

A spectral line has laboratory wavelength 500 nm and is observed from a star at 501 nm. Estimate the radial speed of the star and state its direction of motion.

Using the observed wavelength as the denominator or forgetting that longer wavelength is red shift and recession.

A spectral line has laboratory wavelength 500 nm and is observed from a star at 501 nm. Estimate the radial speed of the star and state its direction of motion.

Choose

Explain Spectral line shifts

A spectral line acts like a wavelength marker. Because each element has known rest wavelengths, astronomers can compare observed line positions with laboratory positions. A uniform shift of the pattern to longer wavelengths is red shift, indicating recession. A shift to shorter wavelengths is blue shift, indicating approach. The shift gives radial velocity, not sideways motion across the sky.

Atoms produce characteristic emission or absorption lines at known laboratory wavelengths.
A Doppler shift moves the whole spectral line pattern relative to its laboratory positions.
If lines shift to longer wavelength, the light is red-shifted and the source is receding.
If lines shift to shorter wavelength, the light is blue-shifted and the source is approaching.
Spectral line shifts measure radial motion: the component of velocity along the line of sight.
Red shifts of distant galaxies are evidence that galaxies are receding from us in an expanding universe model.

Interpret the spectral line shift from laboratory and observed wavelengths.

Graph

The diagram shows laboratory spectral lines above observed spectral lines on a wavelength axis increasing to the right.

1Identify whether the observed wavelengths are longer or shorter.
2Name the shift as red shift or blue shift.
3State whether the source is approaching or receding along the line of sight.

A hydrogen line with laboratory wavelength 486.1 nm is observed in a galaxy spectrum at 492.0 nm. State the type of shift and what it implies about the galaxy motion.

Calling it blue shift because the line is in the visible blue-green region, instead of comparing observed and laboratory wavelengths.

A hydrogen line with laboratory wavelength 486.1 nm is observed in a galaxy spectrum at 492.0 nm. State the type of shift and what it implies about the galaxy motion.

Choose

Model Mechanical-wave Doppler formulas

Mechanical-wave Doppler formula questions are easiest if you decide the physical case first. A moving observer meets wavefronts more or less often, so observer speed changes the numerator. A moving source emits wavefronts closer together or farther apart in the medium, so source speed changes the denominator. After calculating, check the answer qualitatively: approach means higher frequency, recession means lower frequency.

For mechanical waves, the medium matters; use v for wave speed in the medium.
If only the observer moves, use f_obs = f_s(v ± v_o)/v: plus for moving toward the source and minus for moving away.
If only the source moves, use f_obs = f_s v/(v ∓ v_s): use v - v_s for a source moving toward the observer and v + v_s for a source moving away.
Approaching motion must give f_obs greater than f_s; receding motion must give f_obs less than f_s.
A moving source changes wavelength in the medium; a moving observer changes the rate at which wavefronts are encountered.

Build the correct mechanical-wave Doppler formula for moving source or moving observer cases.

Formula
Target formula moving observer: f_obs = f_s (v ± v_o)/v; moving source: f_obs = f_s v/(v ∓ v_s)
f_obs
observed frequency
Hz
f_s
source or emitted frequency
Hz
v
speed of sound or mechanical wave in the medium
m s^-1
v_o
observer speed relative to the medium
m s^-1
v_s
source speed relative to the medium
m s^-1
1Decide whether source or observer motion is responsible.observer motion -> numerator; source motion -> denominator
2For a moving observer and stationary source, choose plus if moving toward and minus if moving away.f_obs = f_s (v ± v_o)/v
3For a moving source and stationary observer, choose v - v_s for approach and v + v_s for recession.f_obs = f_s v/(v ∓ v_s)
4Check the result qualitatively.approach -> f_obs > f_s; recede -> f_obs < f_s

A siren emits sound at 500 Hz while moving toward a stationary observer at 30 m s^-1. The speed of sound is 340 m s^-1. Calculate the observed frequency.

Using the moving-observer formula or choosing v + v_s for a source approaching the observer.

A siren emits sound at 500 Hz while moving toward a stationary observer at 30 m s^-1. The speed of sound is 340 m s^-1. Calculate the observed frequency.

Choose

Retrieve the Core C.5 Doppler effect Model

Review

Core C.5 is mostly a sign and representation topic. Decide whether source and observer are approaching or receding. Then translate that into wavefront spacing, observed wavelength, observed frequency, and spectral line movement. The light approximation uses fractional wavelength shift, while spectral line interpretation tells you the direction of radial motion.

The Doppler effect is a change in observed frequency or wavelength due to relative motion between source and observer.
Approaching motion gives higher observed frequency and shorter observed wavelength; receding motion gives lower observed frequency and longer observed wavelength.
In wavefront diagrams, closer spacing means shorter wavelength and higher frequency; wider spacing means longer wavelength and lower frequency.
For low-speed electromagnetic shifts, z = (λ_obs - λ0)/λ0 ≈ v/c, with positive z for recession.
Spectral lines shifted to longer wavelength show red shift and recession; shifted to shorter wavelength show blue shift and approach.

Match each C.5 core cue to the Doppler interpretation it should trigger.

Match
Reasons
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Retrieve the HL C.5 Doppler effect Model

Review

HL Doppler questions are less about memorizing plus and minus signs and more about choosing the correct physical case. A moving observer changes how often wavefronts are encountered, so its speed appears in the numerator. A moving source changes the wavelength laid down in the medium, so its speed appears in the denominator. The final answer must pass the qualitative approach/recede check.

For mechanical waves, use wave speed in the medium and decide whether the source or observer moves relative to that medium.
Moving observer with stationary source: f_obs = f_s(v ± v_o)/v.
Moving source with stationary observer: f_obs = f_s v/(v ∓ v_s).
Use signs so approaching motion gives f_obs > f_s and receding motion gives f_obs < f_s.
Do not use these mechanical-wave formulas for light; use the low-speed electromagnetic approximation when appropriate.

Match each HL Doppler cue to the correct formula move.

Match
Reasons
0/8