🚗

Doppler Effect Calculator

Use this Doppler effect calculator to find the observed frequency shift when a sound source or observer is moving. Enter the 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)
—

Common Scenarios

Understanding the Doppler Effect

The Doppler effect is the change in frequency of a sound (or any wave) as the source and observer move relative to each other. When approaching, sound waves are compressed, producing a higher observed frequency (higher pitch). When receding, waves are stretched, producing a lower frequency (lower pitch). This Doppler shift is entirely a function of relative velocity — the moving source frequency as emitted (its rest frequency) remains constant throughout. To explore how these shifts translate into musical pitch change, see the wavelength calculator for the corresponding wavelength at any frequency.

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. Color Doppler imaging uses the direction of the shift to distinguish blood flowing toward versus away from the transducer.
  • Astronomical red/blueshift — distant galaxies show redshifted light because they're moving away. This revealed the expanding universe. Cosmological redshift is not purely Doppler in nature (it also includes the expansion of space), but the classical acoustic Doppler formula is the conceptual foundation.
  • 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. The dual-polarization extension also distinguishes rain from hail by comparing horizontal and vertical Doppler returns.
  • Formula 1 and motorsport — the characteristic rising-then-falling pitch of a passing race car is a textbook Doppler demonstration; at 80 m/s (~288 km/h) the shift spans nearly two musical semitones across the flyby.

Note: this calculator uses the classical (non-relativistic) acoustic Doppler formula, which is valid when all speeds are well below the speed of sound. For electromagnetic waves (radar, light) the special-relativistic formula must be used instead. The speed of sound itself varies with temperature — approximately 331 + 0.6 × T(°C) m/s at sea level — so adjust the "Speed of Sound" input for high-altitude or extreme-temperature scenarios. You can verify the underlying speed of sound at your conditions before entering it here, and cross-check supersonic source behavior with the Mach number calculator.

Share or embed this tool

Free to use on your own website — WordPress, Wix, or any platform. Paste one line and it works instantly, resizing to fit.

X Facebook LinkedIn WhatsApp Email

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.
Does the speed of sound change with temperature, and does it affect the result?
Yes — the speed of sound in dry air increases roughly 0.6 m/s per °C. At 0 °C it is approximately 331 m/s; at 20 °C it is about 343 m/s; at 40 °C it rises to around 355 m/s. Because the Doppler formula uses the speed of sound as a reference, using the wrong value for your environment will give an inaccurate observed frequency. Always adjust the "Speed of Sound" input to match your actual air temperature and altitude when precision matters.
Why is the Doppler shift asymmetric — why is moving source different from moving observer?
For sound, the medium (air) provides an absolute reference frame. A moving source physically compresses or stretches the wavelength in the air before the wave reaches you, while a moving observer simply intercepts wave crests at a different rate without altering the wavelength. At the same relative speed, these produce different frequency ratios: f' = f₀ × v/(v−vₛ) for a moving source versus f' = f₀ × (v+v₀)/v for a moving observer. For light there is no medium, so only relative velocity matters and both cases are symmetric.
How big is the Doppler pitch shift for a typical passing car or siren?
A car traveling at 100 km/h (~27.8 m/s) with a 440 Hz horn produces an observed frequency of about 479 Hz approaching and 407 Hz receding — a total flyby swing of roughly 72 Hz, or about 264 cents (more than two semitones). An emergency siren at 50 m/s produces an even wider swing. These real-world numbers confirm why the pitch change of a fast-moving vehicle sounds so dramatic compared to the nearly imperceptible shift from a walking observer.
← All Acoustic Physics Tools