Doppler Effect Physics Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

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.

Solution

  1. 1
    Rearrange the EM Doppler formula: vs=Δf⋅c2fv_s = \frac{\Delta f \cdot c}{2f}.
  2. 2
    vs=3500×3×1082×10.5×109=1.05×10122.1×1010v_s = \frac{3500 \times 3 \times 10^8}{2 \times 10.5 \times 10^9} = \frac{1.05 \times 10^{12}}{2.1 \times 10^{10}}
  3. 3
    vs=50 m/s=180 km/hv_s = 50 \text{ m/s} = 180 \text{ km/h}

Answer

vs=50 m/s=180 km/hv_s = 50 \text{ m/s} = 180 \text{ km/h}
Police radar uses the Doppler effect with electromagnetic waves. The frequency shift is doubled because the wave travels to the car and reflects back, experiencing two Doppler shifts.

About Doppler Effect

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

Learn more about Doppler Effect →

More Doppler Effect Examples

Example 1 easy

An ambulance siren emits sound at [formula]. As the ambulance approaches you at [formula], what freq

Example 2 medium

A train whistle blows at [formula]. You are stationary and hear [formula]. Is the train approaching

Example 3 medium

A car horn emits [formula]. You drive toward the stationary car at [formula]. What frequency do you

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