Doppler Effect Calculator
Frequency heard as a source approaches and as it recedes, with the shift in hertz and semitones.
Results
Frequency
467.245
Hz
Frequency
415.758
Hz
Frequency shift
27.245
Hz
Shift in semitones
1.040
What this tool does
The two results are the drop you hear as an ambulance passes: the first is the approaching pitch, the second is the receding one, and the jump between them happens in the instant it goes by. The semitone figure puts that shift in musical terms — a passing siren often drops more than a whole tone.
Formula
f′ = f × (c + v observer) ÷ (c − v source)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
f | Frequency | Hz |
vs | Source speed | m/s |
vo | Observer speed | m/s |
c | Wave speed | m/s |
FA | Frequency | Hz |
FR | Frequency | Hz |
DF | Frequency shift | Hz |
ST | Shift in semitones | — |
Worked example
- Frequency440 Hz
- Source speed20 m/s
- Observer speed0 m/s
- Wave speed343 m/s
- Frequency467.245 Hz
- Frequency415.758 Hz
- Frequency shift27.245 Hz
- Shift in semitones1.040
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.