Doppler Shift Calculator
Enter source frequency, wave speed and relative velocities to compute the observed frequency, shift and wavelength via the Doppler effect.
Input Data
Results
At a glance:The Doppler effect is the change in observed frequency of a wave due to relative motion of source and observer. For motion along the line of sight, f' = f·(v + v_o)/(v − v_s), with v the wave speed in the medium, v_o the observer's speed toward the source (positive when approaching) and v_s the source's speed toward the observer (positive when approaching). Approaching raises the frequency (blueshift); receding lowers it (redshift). The shift Δf = f' − f; wavelength λ' = v/f'. For light (no medium) use the relativistic formula f' = f·√((1+β)/(1−β)) with β = v/c. This tool uses the classical wave form.
Formula
Classical: f' = f·(v + v_o)/(v − v_s)
Shift: Δf = f' − f
Wavelength: λ' = v/f'
How to Use
- Enter the source frequency f and wave speed v.
- Enter observer speed toward source and source speed toward observer.
- The calculator returns f', Δf, shift % and λ'.
Case Studies
Passing ambulance
f = 700 Hz, v = 343 m/s, source approaches at 30 m/s.
f' = 700×343/(343−30) ≈ 767 Hz.
After passing (receding) f' ≈ 643 Hz — the familiar drop.
FAQ
Why does an approaching siren sound higher?
The source moves toward you, compressing wavefronts so you receive a higher frequency (f' > f) while it approaches; after it passes, the frequency drops.
Does this apply to light?
The classical formula needs the medium's wave speed, which light lacks; for electromagnetic waves use the relativistic Doppler formula with β = v/c.
Related Tools
References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.