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Doppler Effect Calculator

This Doppler effect calculator turns source frequency, speeds and the speed of sound into the frequency you hear. Example: a 700 Hz siren approaching at 90 km/h sounds like 755 Hz, and like about 652 Hz as it moves away.

Example: Source frequency 700 Hz · Motion of the source: Source approaches · Speed of the source 90 · Motion of the observer: Observer at rest · Speed of the observer 0 · Unit of the speeds: Kilometres per hour (km/h) · Air temperature 20 °C → Result: Heard frequency: 754.99 Hz (+54.994 Hz). Source: Wikipedia – Doppler-Effekt. Updated: .

Hz
Magnitude of the speed; the direction is chosen above. The source must be slower than sound.
°C
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Result

Result
Heard frequency: 754.99 Hz (+54.994 Hz)
Frequency and wavelength
ItemValue
Source frequency700 Hz
Heard frequency754.99 Hz
Frequency ratio f′/f1.0786
Pitch change (semitones)+1.3093
Wavelength (source → observer)0.49031 m → 0.45459 m
Speed of sound343.21 m/s
Mach number of the source0.072841
Pass-by: before and after
PhaseHeard frequencyChange
Source approaches754.99 Hz+54.994 Hz
Source moves away652.47 Hz−47.527 Hz
Steps
  • Speed of sound in air at 20 °C: c = 331.3 m/s · √(1 + T / 273.15 K) = 343.21 m/s.
  • Heard frequency f′ = f · (c + v_O) / (c − v_S) = 700 · (c + 0) / (c − 25) = 754.99 Hz.
  • Signs: if source and observer move toward each other the frequency rises, if they move apart it falls.
Valid for sound in still air with motion along the line joining source and observer. For light and very high speeds the relativistic formula applies; if the air moves (wind), the speeds change relative to the medium.

How it is calculated

The Doppler effect describes how the perceived frequency of a wave changes when the source or the observer moves. With sound you hear it from passing sirens: the tone is higher while approaching and lower while moving away.

The formula

For sound in still air, f′ = f · (c + v_O) / (c − v_S). Here f is the source frequency, c the speed of sound, v_S the source speed and v_O the observer speed. When the source approaches, v_S is positive in the denominator and makes it smaller, so the frequency rises; moving away reverses the sign. The speed of sound in air follows from temperature: c = 331.3 m/s · √(1 + T / 273.15 K), about 343 m/s at 20 °C.

Siren example

An ambulance at 90 km/h (25 m/s) with a 700 Hz siren: approaching you hear 700 · 343.2 / (343.2 − 25) ≈ 755 Hz, moving away 700 · 343.2 / (343.2 + 25) ≈ 652 Hz. The pass-by table shows both values; the jump is about 2.5 semitones.

Frequently asked questions

How do you calculate the Doppler effect?

With f′ = f · (c + v_O) / (c − v_S): source frequency times speed of sound plus observer speed, divided by speed of sound minus source speed. Speeds are positive for approach.

Why does a siren sound lower as it passes?

While approaching, the sound waves are compressed and the frequency rises; while moving away they are stretched and the frequency falls. At the moment of passing the pitch therefore drops.

Does the formula also apply to light?

No. Light needs no medium; for light the relativistic Doppler effect applies, which causes red or blue shift. This calculator covers sound only.

Sources and legal basis

As of: · Editorial policy

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