Physics · Waves

Doppler Effect

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Wrap-up

What you learned

Recommended next: Open concept testCheck whether the core ideas are ready without leaving this concept.
Read next: Wave InterferenceCombine waves after you can track one moving source

Key takeaway

Source motion changes wavefront spacing in the medium: compressed ahead and stretched behind.
Observer motion changes the arrival rate at the listener without changing the emitted frequency.
A higher or lower heard pitch is a crest-arrival-rate change, not proof that the source changed its tone.

Common misconception

A moving siren must emit a different frequency in front than behind.

The emitted frequency stays fixed here. What changes is the spacing in the medium and the rate at which the observer meets those wavefronts.

Keep the sound story moving

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Combine sound sourcesWaves

Wave Interference

Superpose two coherent sources, trace their path difference to phase difference, and watch bright and dark regions emerge on the same live screen.

Resonant patternsWaves

Standing Waves

Track fixed nodes, moving antinodes, and harmonic mode shapes on one live string while the same probe trace shows the underlying oscillation in time.

Review the medium modelSound

Sound Waves and Longitudinal Motion

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Equation snapshotSpacing ahead of the moving source · Spacing behind the moving sourceShow 3 equations

Read the spacing equations first, then use the observed-frequency equation to add observer motion.

Spacing ahead of the moving source
$λ_{ah e a d} = \frac{v _{w a v e} - v _{s}}{f _{s}}$
Ahead of the moving source, each new crest is emitted from a more forward position, so the spacing in the medium is smaller.
Spacing behind the moving source
$λ_{b e hin d} = \frac{v _{w a v e} + v _{s}}{f _{s}}$
Behind the moving source, each new crest is emitted farther ahead than the previous one, so the spacing in the medium is larger.
Observed frequency in one medium
$f_{o b s} = f_{s} \frac{v _{w a v e} + v _{o}}{v _{w a v e} - d v _{s}}$
The denominator comes from the spacing laid down by the moving source on the chosen side, while the numerator comes from how quickly the observer meets those wavefronts.

Why it behaves this way

Explanation

The Doppler effect does not mean the source changes how often it emits. In this model the emitted frequency stays fixed. What changes first is the spacing laid down in the medium: ahead of a moving source, wavefronts are packed closer together, while behind it they are spread farther apart.

Observer motion then changes how quickly those wavefronts are met on the chosen side. A listener moving toward the source encounters them more often, while a listener moving away encounters them less often. This bench keeps the circles, spacing guides, and heard-frequency trace tied to the same pass-by scene, so a higher heard pitch means a higher arrival rate, not a hidden change in the emitted tone.

Key ideas

01A moving source changes the spacing laid down in the medium: compressed ahead, stretched behind.

02A moving observer changes how quickly wavefronts are encountered, but it does not change the spacing already present in the medium.

03In this classical sound model, a higher heard pitch means wavefronts arrive more often, not that the source started emitting faster.

Worked examples

Live Doppler checks

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Frozen walkthrough

These checks use the same moving-source setup shown on the stage and graphs, so each formula stays tied to one honest pass-by situation.

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Example 1 of 2

Frozen valuesUsing frozen parameters

For this moving-source setup with $v_{w a v e} = 3.2 m/s$ , $f_{s} = 1.1 Hz$ , and $v_{s} = 0.55 m/s$ , what spacing is laid down ahead of the source and behind it?

v_{w a v e}

Wave speed

3.2 m/s

f_{s}

Source frequency

1.1 Hz

v_{s}

Source speed

0.55 m/s

λ_{ah e a d}

Front spacing

2.41 m

λ_{b e hin d}

Rear spacing

3.41 m

1. Use the moving-source spacing relations

Use

λ_{ah e a d} = \frac{v _{w a v e} - v _{s}}{f _{s}}

and

λ_{b e hin d} = \frac{v _{w a v e} + v _{s}}{f _{s}}

2. Substitute the setup source values

λ_{ah e a d} = \frac{3.2 - 0.55}{1.1} = 2.41 m

and

λ_{b e hin d} = \frac{3.2 + 0.55}{1.1} = 3.41 m

3. Read the spacing split

The source is launching each later crest from a farther-forward position, so the front spacing becomes 2.41 m while the rear spacing stretches to 3.41 m.

Spacing result

λ_{ah e a d} = 2.41 m, λ_{b e hin d} = 3.41 m

The source moves forward between emissions, so the front wavefront spacing is compressed while the rear spacing stretches.

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Accessibility

Open the text-first descriptions when you need the simulation and graph translated into words.

The simulation shows one sound source moving through a horizontal medium and one observer listening either ahead of the source or behind it. Expanding wavefronts, spacing markers, motion arrows, and arrival labels all stay linked on the same bench.

Changing source speed changes the spacing laid down in the medium. Changing observer speed changes how fast the observer meets those wavefronts. Both effects update the same bench and graphs.

Graph summary

The first graph compares the emitted source signal with the observer signal over time.

The second graph shows how source speed changes front and rear spacing, and the third graph shows how observer speed changes heard frequency on the chosen side relative to the emitted-frequency baseline.

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Starter track

Step 4 of 5

Sound and Acoustics

Doppler Effect appears later in this track, so it is cleaner to start from the beginning first.

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Also appears in Waves.

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