The Doppler effect is the change in frequency you notice when a source of waves and an observer move relative to each other. It is why a passing train horn drops in pitch, how police radar measures speed and how astronomers know the universe is expanding. This calculator handles both kinds of waves. For sound, it accounts for a moving source, a moving listener and the speed of sound in the medium. For light and radio waves, it uses the relativistic formula and reports the redshift or blueshift.
How to use the Doppler effect calculator
- Choose the Type of wave: sound, which travels through a medium, or light/radio.
- Pick what to Solve for: the observed frequency, the emitted frequency, or a speed.
- For sound, choose the Medium: air (enter its temperature), fresh water, seawater or a custom wave speed.
- Enter the known frequencies and speeds. Speeds are positive when the source and observer approach each other and negative when they separate.
- Read the result, the frequency shift in hertz, percent and musical semitones, and, for a moving source, the pitch you would hear after it passes.
Doppler effect formulas
For sound in a medium with wave speed c:
fs is the emitted frequency, fo the observed one, vo the observer’s speed toward the source and vs the source’s speed toward the observer. The calculator rearranges this to find any one of the four.
For light, with relative approach speed v and β = v ÷ c:
Redshift is defined as z = fs ÷ fo − 1, positive for receding sources.
Worked example
An ambulance siren
A siren emits 700 Hz and approaches a standing listener at 25 m/s (90 km/h). The air is 20 °C, so c = 331.3 × √(1 + 20/273.15) = 343.2 m/s.
fo = 700 × 343.2 ÷ (343.2 − 25) = 755.0 Hz
After it passes and recedes at the same speed, the listener hears 700 × 343.2 ÷ (343.2 + 25) = 652.5 Hz. The drop from 755 to 652 Hz is about 2.5 semitones, the familiar "eee-yow".
Finding a speed. A 1,000 Hz horn on a moving car is heard at 1,080 Hz by a stationary listener in 20 °C air. Solve for source speed: vs = 343.2 − 1,000 × 343.2 ÷ 1,080 = 25.4 m/s, about 91.5 km/h or 56.9 mph.
Doppler shifts in everyday technology
| Application | Wave | What the shift reveals |
|---|---|---|
| Police radar and speed guns | Microwaves (about 24 GHz) | Vehicle speed |
| Weather radar | Microwaves | Wind and rotation in storms |
| Medical ultrasound | Sound, 2–15 MHz | Blood flow speed and direction |
| Bat and dolphin echolocation | Ultrasound | Whether prey is approaching |
| Astronomy | Visible light | Star and galaxy motion, exoplanets |
Radar and ultrasound detect a reflected wave, which is shifted twice: once on the way to the moving target and once on the way back. For a target much slower than the wave, the total shift is roughly twice the one-way value.
Light: redshift and blueshift
Hydrogen atoms emit red light at 656.28 nm (456.81 THz). If a star’s hydrogen line appears at 656.20 nm, the star is approaching at about 33 km/s. Edwin Hubble’s observation that distant galaxies show redshifts that grow with distance was the first evidence that the universe is expanding. For very large cosmological redshifts the relativistic Doppler formula is only an approximation, because space itself stretches.
Assumptions
The sound formula assumes still air and motion along the line between source and observer; for motion at an angle, use the component of velocity along that line, which is why a passing siren’s pitch slides smoothly rather than jumping. Wind adds to or subtracts from the effective wave speed. To convert a frequency to a wavelength, use the wavelength calculator; to see how loud a source is at a distance, use the decibel calculator.
Frequently asked questions
Why does a siren sound higher as it approaches and lower as it leaves?
While the ambulance moves toward you, each wave crest is emitted a little closer than the last, so crests arrive more often and the pitch rises. After it passes, the crests are spread out. A 700 Hz siren at 25 m/s is heard at about 755 Hz approaching and 652 Hz receding in 20 °C air.
Which sign should I use for the speeds?
Positive when the source and observer move toward each other, negative when they move apart. The source speed is the source's own motion and the observer speed is the listener's, both measured relative to still air.
Why does the air temperature matter?
The speed of sound depends on temperature: about 331 m/s at 0 °C, 343 m/s at 20 °C and 349 m/s at 30 °C. The calculator uses 331.3 × √(1 + T/273.15) for dry air, and you can switch to fresh water, seawater or a custom wave speed.
What happens when the source moves faster than sound?
The waves in front of it pile up into a shock wave, heard as a sonic boom, and there is no ordinary Doppler-shifted tone ahead of the source. The calculator refuses source speeds at or above the wave speed for that reason.
How is the Doppler effect for light different?
Light needs no medium, so only the relative speed matters, and special relativity adds time dilation. The calculator uses f₀ = fₛ√((1 + β)/(1 − β)) with β = v/c. Receding galaxies show redshift; approaching stars show blueshift.