Doppler Shift Calculator
Heard pitch of a moving siren from source speed and direction.
What it does
Every passing ambulance demonstrates the Doppler effect. Its siren never changes pitch at the source, yet listeners hear it slide from high to low as it passes. Motion squeezes the waves ahead of the source and stretches the ones behind, and ears read wavelength as pitch.
The tool above computes the heard frequency for a stationary listener. Enter the source frequency in Hz, the source speed in m/s or mph, and whether it nears or leaves. The default 440 Hz siren approaching at 30 m/s arrives at 482.2 Hz, a lift of 42.2 Hz.
The equations follow NASA Glenn classroom pages and OpenStax physics: approaching frequency equals source times sound speed over (sound speed minus source speed), with a plus sign for retreat. Both use 343 m/s for air near room temperature, the standard in textbook examples.
The model stays deliberately narrow. Listeners stand still, wind stays calm, speeds stay subsonic, and sound speed stays fixed instead of tracking temperature. Moving listeners, supersonic cracks, and light wave redshifts each need their own pages.
How to use
- Pick metric or imperial for the speed entry.
- Type the true source frequency in Hz.
- Choose toward or away motion.
- Type the source speed along the line to the listener.
- Read the heard frequency first, then the plus or minus shift.
- Flip direction to hear the pass by drop.
Formula
- f
- True source frequency in Hz.
- c
- Speed of sound, fixed at 343 m/s here.
- vs
- Source speed toward or away along the sight line.
- shift
- Heard minus true frequency in Hz.
Only the line of sight component counts: crossing traffic barely shifts. Faster sources shift more, and higher source notes shift more hertz at the same speed. As source speed nears 343 m/s the denominator shrinks toward zero, which is the mathematical seed of the sonic boom.
Worked example
Example: 440 Hz siren nearing at 30 m/s
Defaults already filled in the form.
- Denominator: 343 - 30 = 313.
- Ratio: 343 / 313 = 1.09585.
- Heard: 440 x 1.09585 = 482.17, shown as 482.2 Hz.
- Shift: 482.17 - 440 = +42.2 Hz.
- Imperial check: 67.1 mph converts to the same speed and repeats 482.2 Hz.
- Flip to recede: 440 x 343 / 373 = 404.6 Hz, a drop of 35.4 Hz.
Reference table
| Source speed | Nearing | Leaving |
|---|---|---|
| 10 m/s | 453.2 Hz | 427.6 Hz |
| 20 m/s | 467.2 Hz | 415.8 Hz |
| 30 m/s | 482.2 Hz | 404.6 Hz |
| 60 m/s | 533.2 Hz | 374.5 Hz |
Limits
- Stationary listener only; moving ears add their own term.
- Subsonic sources; supersonic flight needs shock wave math.
- Fixed 343 m/s ignores temperature, altitude, and wind.
- Straight line motion assumed; angled paths use the closing component.
Common mistakes
- Using km/h or mph figures as m/s without the toggle.
- Expecting the siren itself to change; only the heard pitch moves.
- Applying sound formulas to light, where relativity rules instead.
- Forgetting the shift scales with the source note, not just speed.
- Reading boom loudness from a frequency page.
Try it yourself
Quick checks. Answers sit tucked under each question.
500 Hz horn leaving at 20 m/s. Heard?
500 x 343 / 363 = 472.5 Hz, a shift of -27.5 Hz.
Same horn nearing at 20 m/s?
500 x 343 / 323 = 531.0 Hz, up 31 Hz.
Why is the rise bigger than the drop at equal speed?
The denominator shrinks one way (343 - v) and grows the other (343 + v).
Questions
What is the Doppler effect?
Pitch change from relative motion bunching or stretching waves.
Does the source change?
No. Emitted frequency stays fixed; travel geometry changes arrival rate.
What speed of sound is used?
343 m/s, still air near 20 C, stated in every result.
What happens at Mach 1?
Waves pile into a shock front heard as a sonic boom; this page refuses those speeds.
Do light waves do this?
Yes, as red and blue shifts, but the formula differs at high speeds.
Where is Doppler used?
Radar guns, medical ultrasound, weather radar, and galaxy speed measurements.