Waves & Optics
Doppler Effect Calculator
Calculate the observed frequency when source and observer are moving relative to each other.
Observed Frequency
f' = f₀(v ± vo)/(v ∓ vs)
Frequency Shift |Δf|
—
Hz
f'/f₀ Ratio
—
×
Step-by-Step Solution
What is the Doppler Effect?
The Doppler effect is the change in frequency of a wave perceived by an observer when the source and observer are moving relative to each other. When approaching, the observed frequency is higher (blue shift). When receding, it is lower (red shift). You hear this every time an ambulance passes.
f' = f₀(v ± v_observer) / (v ∓ v_source)
Upper signs: approaching | Lower signs: receding | v = wave speed in medium
Variables Explained
| Symbol | Name | Unit | Notes |
|---|---|---|---|
| f' | Observed Frequency | Hz | Frequency heard/detected by the observer |
| f₀ | Source Frequency | Hz | Frequency emitted by the source at rest |
| v | Wave Speed | m/s | 343 m/s for sound in air at 20°C; 3×10⁸ m/s for light |
| v_o | Observer Speed | m/s | Speed of the observer toward (+) or away (−) from source |
| v_s | Source Speed | m/s | Speed of the source toward (−) or away (+) from observer |
💡 For light, the Doppler effect is used in astronomy to determine whether stars are moving toward (blue shift) or away from (red shift) Earth. This helped Edwin Hubble discover that the universe is expanding.
Frequently Asked Questions
Why does an ambulance siren change pitch as it passes?
As the ambulance approaches, it "catches up" with the sound waves it emits, compressing them in front — raising the frequency. As it recedes, the waves stretch out behind it, lowering the frequency. The pitch drops suddenly as it passes.
How does radar use the Doppler effect?
Radar guns emit a known frequency. The frequency of the reflected wave from a moving car is slightly different due to the Doppler effect. The speed is calculated from the frequency shift.
What is the red shift?
Red shift is the Doppler effect applied to light from distant galaxies moving away from us. Their light is stretched to longer (redder) wavelengths. Hubble observed that almost all galaxies are red-shifted, proving the universe is expanding.