Practice Doppler Effect in Physics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick 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.

Showing a random 20 of 50 problems.

Example 1

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

Example 2

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

Example 3

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 4

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

Example 5

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 6

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

Example 7

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 8

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 9

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 10

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 11

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

Example 12

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 13

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

Example 14

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 15

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 16

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 17

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 18

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 19

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

Example 20

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