Doppler Effect Examples in Physics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Doppler Effect.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

The change in the observed frequency (and wavelength) of a wave when the source and the observer are in relative motion.

An ambulance siren sounds higher-pitched approaching, lower-pitched receding.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Doppler Effect asks what oscillates, what travels, and which wave quantity is being measured.

Common stuck point: Students often know a formula related to doppler effect but skip the recognition step: Am I describing a repeating disturbance using wavelength, frequency, amplitude, speed, medium, or superposition? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Am I describing a repeating disturbance using wavelength, frequency, amplitude, speed, medium, or superposition?

Worked Examples

Example 1

easy
An ambulance siren emits sound at 700 Hz700 \text{ Hz}. As the ambulance approaches you at 30 m/s30 \text{ m/s}, what frequency do you hear? Use vsound=340 m/sv_{\text{sound}} = 340 \text{ m/s}.

Answer

f′≈768 Hzf' \approx 768 \text{ Hz}

First step

1
Doppler effect for approaching source: f′=f×vv−vsf' = f \times \frac{v}{v - v_s}.

Full solution

  1. 2
    f′=700×340340−30=700×340310f' = 700 \times \frac{340}{340 - 30} = 700 \times \frac{340}{310}
  2. 3
    f′=700×1.097≈768 Hzf' = 700 \times 1.097 \approx 768 \text{ Hz}
The Doppler effect causes the perceived frequency to increase when a sound source approaches and decrease when it moves away. This is why an ambulance siren sounds higher-pitched as it approaches.

Example 2

medium
A train whistle blows at 500 Hz500 \text{ Hz}. You are stationary and hear 475 Hz475 \text{ Hz}. Is the train approaching or moving away? What is the train's speed? Use vsound=340 m/sv_{\text{sound}} = 340 \text{ m/s}.

Example 3

medium
A source emits at f=800f = 800 Hz and moves toward a stationary observer at vs=40v_s = 40 m/s; speed of sound v=340v = 340 m/s. Find observed frequency.

Example 4

medium
A stationary source emits f=600f = 600 Hz; observer drives away at vo=30v_o = 30 m/s; v=340v = 340 m/s. Find f′f'.

Example 5

hard
Both source and observer approach each other: f=500f = 500 Hz, vs=20v_s = 20 m/s, vo=10v_o = 10 m/s, v=340v = 340 m/s. Find observed frequency.

Example 6

hard
A stationary source emits f=1f = 1 kHz; the wind blows from source to observer at w=10w = 10 m/s; still-air sound speed v=340v = 340 m/s. The observer is stationary. Find f′f'.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium
A car horn emits 400 Hz400 \text{ Hz}. You drive toward the stationary car at 20 m/s20 \text{ m/s}. What frequency do you hear? Use vsound=340 m/sv_{\text{sound}} = 340 \text{ m/s}.

Example 2

hard
Police radar emits microwaves at 10.5 GHz10.5 \text{ GHz}. The reflected signal from an approaching car has a frequency shift of 3500 Hz3500 \text{ Hz}. What is the car's speed? Use c=3×108 m/sc = 3 \times 10^8 \text{ m/s} and the Doppler formula Δf=2vsfc\Delta f = \frac{2v_s f}{c} for electromagnetic waves.

Example 3

easy
An ambulance siren approaches you. Does the pitch you hear rise or fall?

Example 4

easy
An ambulance siren moves away from you. Does the observed pitch rise or fall?

Example 5

easy
Does the Doppler effect change the frequency actually emitted by the source?

Example 6

easy
Light from a distant galaxy is shifted to lower frequency (redshift). Is the galaxy approaching or receding?

Example 7

easy
Light from a star is shifted to higher frequency (blueshift). Approaching or receding?

Example 8

easy
The Doppler effect requires what condition between source and observer?

Example 9

easy
A stationary source emits a tone at 500500 Hz. You stand still beside it. What frequency do you hear?

Example 10

easy
As a source moves toward you, what happens to the wavelength of the sound that reaches you?

Example 11

medium
A source emits f=500f = 500 Hz and moves toward a stationary observer at vs=34v_s = 34 m/s; sound speed v=340v = 340 m/s. Find the observed frequency using f′=f v/(v−vs)f' = f\,v/(v - v_s).

Example 12

medium
Same source (f=500f = 500 Hz, vs=34v_s = 34 m/s) now moves away; v=340v = 340 m/s. Use f′=f v/(v+vs)f' = f\,v/(v + v_s).

Example 13

medium
An observer moves toward a stationary source (f=400f = 400 Hz) at vo=34v_o = 34 m/s; v=340v = 340 m/s. Use f′=f (v+vo)/vf' = f\,(v + v_o)/v.

Example 14

medium
An observer moves away from a stationary source (f=400f = 400 Hz) at vo=34v_o = 34 m/s; v=340v = 340 m/s. Use f′=f (v−vo)/vf' = f\,(v - v_o)/v.

Example 15

medium
A bat emits f=50f = 50 kHz toward a wall and approaches at vs=17v_s = 17 m/s; v=340v = 340 m/s. Find the frequency striking the wall using f′=f v/(v−vs)f' = f\,v/(v - v_s).

Example 16

medium
Why can't you use the simple sound Doppler formula for light from a fast-moving star?

Example 17

medium
A car horn sounds higher as it nears and lower as it passes. At the instant it is exactly alongside you (closest point), is there a shift?

Example 18

medium
A train whistle emits f=600f = 600 Hz and moves toward a stationary observer at vs=20v_s = 20 m/s; v=340v = 340 m/s. Find the observed frequency using f′=f v/(v−vs)f' = f\,v/(v - v_s).

Example 19

medium
A train whistle (f=600f = 600 Hz) now recedes at vs=20v_s = 20 m/s; v=340v = 340 m/s. Use f′=f v/(v+vs)f' = f\,v/(v + v_s).

Example 20

challenge
A source (f=600f = 600 Hz) moves toward an observer who also moves toward the source. v=340v = 340, vs=20v_s = 20, vo=20v_o = 20 m/s. Use f′=f (v+vo)/(v−vs)f' = f\,(v + v_o)/(v - v_s).

Example 21

challenge
A source (f=680f = 680 Hz) recedes at vs=20v_s = 20 m/s while the observer approaches at vo=20v_o = 20 m/s; v=340v = 340 m/s. Use f′=f (v+vo)/(v+vs)f' = f\,(v + v_o)/(v + v_s).

Example 22

challenge
A sound source approaches a wall at vs=34v_s = 34 m/s emitting f=500f = 500 Hz (v=340v = 340 m/s). The wall reflects the sound back to the moving source. The wall first receives f1=f v/(v−vs)f_1 = f\,v/(v - v_s); it then re-emits f1f_1 and the approaching source (now observer) hears f2=f1(v+vs)/vf_2 = f_1(v + v_s)/v. Find f2f_2.

Example 23

easy
A motorcycle revs while parked. You walk toward it at constant speed. Do you hear the engine higher or lower?

Example 24

easy
A distant galaxy's spectral lines are shifted to longer wavelengths. Which way is it moving relative to Earth?

Example 25

easy
A police siren whose pitch you hear keeps dropping. Is the car approaching or moving away?

Example 26

easy
A boat sits still while a buoy moves toward it. Will the boat measure a Doppler shift in the waves from the buoy's bobbing?

Example 27

medium
A source (f=800f = 800 Hz) recedes at vs=40v_s = 40 m/s from a stationary observer; v=340v = 340 m/s. Find f′f'.

Example 28

medium
A stationary source emits f=600f = 600 Hz; an observer drives toward it at vo=30v_o = 30 m/s; v=340v = 340 m/s. Find f′f'.

Example 29

medium
A train whistle emits f=750f = 750 Hz and approaches you at vs=25v_s = 25 m/s; v=340v = 340 m/s. What frequency do you hear?

Example 30

medium
A car horn f=500f = 500 Hz; the observer cycles toward the parked car at vo=5v_o = 5 m/s; v=340v = 340 m/s. Find observed frequency.

Example 31

medium
A stationary observer hears f′=550f' = 550 Hz from a source emitting f=500f = 500 Hz; v=340v = 340 m/s. Is the source approaching or receding, and at what speed?

Example 32

medium
A whistle emits at 400400 Hz; a runner moves away at 55 m/s; v=340v = 340 m/s. Find observed frequency.

Example 33

hard
Source approaches at vs=15v_s = 15 m/s; observer recedes at vo=10v_o = 10 m/s; f=600f = 600 Hz, v=340v = 340 m/s. Find f′f'.

Example 34

hard
A radar beam at f0=24f_0 = 24 GHz reflects from a car approaching at v=20v = 20 m/s. Find the round-trip Doppler shift Δf=2vf0/c\Delta f = 2 v f_0 / c.

Example 35

hard
A bat emits 4040 kHz toward an insect moving away at 55 m/s; v=340v = 340 m/s. Find the frequency the insect 'hears' using f′=f(v−vo)/vf' = f(v - v_o)/v.

Example 36

hard
A train whistle emits f=500f = 500 Hz; the train approaches a wall at vs=17v_s = 17 m/s; v=340v = 340 m/s. Find the frequency arriving at the wall.

Example 37

hard
A spectral line at λ0=656.3\lambda_0 = 656.3 nm is observed at λ=657.6\lambda = 657.6 nm from a galaxy. Using v/c≈Δλ/λ0v/c \approx \Delta\lambda/\lambda_0, find its recession speed.

Example 38

challenge
Two cars travel directly toward each other on a road; each at v=25v = 25 m/s. Car A's horn emits f=450f = 450 Hz; vsnd=340v_{snd} = 340 m/s. What frequency does car B hear?

Example 39

challenge
A source emits f=500f = 500 Hz from a stationary point. The observer moves transverse to the line of sight at vo=30v_o = 30 m/s (not toward or away). Using the classical sound Doppler effect, what frequency is heard?
← Back to Doppler Effect Formula Explained Practice Mode

Background Knowledge

These ideas may be useful before you work through the harder examples.

frequencywave speed