Paritian

Physics

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

SymbolMeaningUnit
fFrequencyHz
vsSource speedm/s
voObserver speedm/s
cWave speedm/s
FAFrequencyHz
FRFrequencyHz
DFFrequency shiftHz
STShift 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.