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Doppler Effect Calculator
Calculate the observed frequency shift when a sound source or observer is moving. Enter source frequency and velocities to get the apparent frequency heard by the observer.
Parameters
Hz
m/s
Source Motion
m/s
Observer Motion
m/s
Observed Frequency
Apparent Frequency (f')
484.1
Hz
Shift (Hz)
+44.1
Shift (cents)
+168
Ratio f'/f₀
1.100
Shift (%)
+10.0%
Doppler Formula
f' = f₀ × (v ± v₀) / (v ∓ vₛ)
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Common Scenarios
Understanding the Doppler Effect
The Doppler effect is the change in frequency of a wave as the source and observer move relative to each other. When approaching, sound waves are compressed → higher frequency (higher pitch). When receding, waves are stretched → lower frequency (lower pitch).
General Doppler Formula
f' = f₀ × (v + v₀) / (v − vₛ)
Use + v₀ when observer moves toward source, − v₀ away. Use − vₛ when source moves toward observer, + vₛ away. v = speed of sound, vₛ must be less than v.
Source Approaching (Observer Still)
f' = f₀ × v / (v − vₛ)
A police siren at 800 Hz approaching at 30 m/s: f' = 800 × 343 / (343 − 30) = 800 × 1.096 = 876.8 Hz
Source Receding (Observer Still)
f' = f₀ × v / (v + vₛ)
Same siren at 800 Hz receding at 30 m/s: f' = 800 × 343 / (343 + 30) = 800 × 0.919 = 735.4 Hz. The total "flyby shift" is 876.8 − 735.4 = 141.4 Hz.
Observer Moving (Source Still)
f' = f₀ × (v ± v₀) / v
An observer walking toward a 440 Hz source at 1.5 m/s: f' = 440 × (343 + 1.5) / 343 = 441.9 Hz — a very small shift because human walking speed is tiny relative to sound speed.
Real-World Applications
- Radar speed guns — measure vehicle speed by analyzing the Doppler shift of reflected radio waves. The formula translates directly from sound to EM waves.
- Medical ultrasound — Doppler ultrasound measures blood flow velocity by detecting frequency shifts of sound reflected off moving blood cells.
- Astronomical red/blueshift — distant galaxies show redshifted light because they're moving away. This revealed the expanding universe.
- Sonar — submarines use Doppler shift to detect whether a target is approaching or receding and estimate its speed.
- Weather radar — Doppler weather radar tracks wind speed and direction by measuring frequency shifts of reflected pulses.
Frequently Asked Questions
Why does a siren sound higher when approaching and lower when receding?
When the source moves toward you, each successive sound wave is emitted slightly closer to you, compressing the wave crests and increasing the frequency. When receding, waves are stretched apart, lowering the frequency. The effect is purely geometric — the siren's actual frequency doesn't change.
What happens when the source speed equals the speed of sound?
At exactly Mach 1, the denominator in the Doppler formula (v − vₛ) becomes zero, meaning the observed frequency would theoretically approach infinity. In practice, all the emitted waves pile up into a shock wave (sonic boom). The Doppler formula no longer applies beyond Mach 1 — supersonic physics requires a different treatment.
Is the Doppler formula the same for light and sound?
Similar but not identical. For sound, the formula depends on whether the source or observer is moving (they are not interchangeable). For light (electromagnetic waves), the relativistic Doppler formula treats both symmetrically because the speed of light is constant in all reference frames: f' = f₀ × √((1+β)/(1−β)) where β = v/c.
How do I calculate frequency shift in cents?
Cents = 1200 × log₂(f'/f₀). This converts the frequency ratio to a musical interval where 100 cents = 1 semitone, 1200 cents = 1 octave. A 10% frequency increase corresponds to about 165 cents — roughly 1.5 semitones above the original pitch.