# Doppler Effect Calculator (Frequency Shift) Compute observed frequency and frequency shift for a moving source and/or observer > Canonical page: https://elysiatools.com/en/tools/doppler-effect-calculator - **Category:** Math & Numbers - **Keywords:** doppler effect, doppler shift, frequency shift, observed frequency, wave, sound, redshift, blueshift, approaching, receding, physics, acoustics ## Overview The Doppler effect is the change in frequency of a wave relative to an observer moving relative to the source. Classical formula: f' = f · (v ± v_o) / (v ∓ v_s) Sign convention: - +v_o when observer approaches; −v_o when receding. - −v_s when source approaches; +v_s when receding. Derived: Δf = f' − f, wavelength ahead = (v − v_s)/f, behind = (v + v_s)/f. Classical formula (sound). For light at relativistic speeds use the relativistic formula. If v_s ≥ v, a shock wave forms. ## Inputs - **Source Frequency (f, Hz)** (number): e.g. 440 (musical A) - **Medium (preset v)** (select) - **Wave Speed (v, m/s)** (number): auto-filled from medium; override when Custom - **Source Motion** (select) - **Source Speed (v_s, m/s)** (number): e.g. 30 (must be < v) - **Observer Motion** (select) - **Observer Speed (v_o, m/s)** (number): e.g. 0 (observer stationary) ## When to use - When analyzing acoustic frequency shifts of moving vehicles, such as sirens or trains, passing a stationary or moving observer. - When calculating wave propagation changes in different media like water or steel for physics and engineering problems. - When teaching or studying classical wave mechanics to determine how relative velocity affects perceived pitch and wavelength. ## How it works - Enter the original source frequency in Hertz and select the propagation medium or input a custom wave speed. - Specify the motion type (stationary, approaching, or receding) and speed for both the wave source and the observer. - The calculator applies the classical Doppler formula, adjusting signs based on whether the entities are approaching or receding. - View the calculated observed frequency, the total frequency shift, and the compressed or stretched wavelengths. ## Use cases - Calculating the pitch shift of an emergency vehicle siren as it approaches and passes a pedestrian. - Determining frequency changes in underwater sonar systems when tracking moving targets. - Solving physics homework problems involving acoustic Doppler shifts and wavelength compression. ## Frequently asked questions ### What is the classical Doppler effect formula used here? It uses f' = f * (v ± v_o) / (v ∓ v_s), where v is wave speed, v_o is observer speed, and v_s is source speed. ### How do the signs change for approaching versus receding motion? The observer speed is added (+) when approaching and subtracted (-) when receding. The source speed is subtracted (-) when approaching and added (+) when receding. ### Can I calculate the Doppler effect for light waves? Yes, by selecting the light preset, though this calculator uses the classical formula rather than the relativistic Doppler formula. ### What happens if the source speed exceeds the wave speed? If the source speed is equal to or greater than the wave speed, a shock wave forms, and the classical formula is no longer valid. ### Does this calculator compute wavelengths? Yes, it calculates the shortened wavelength ahead of the moving source and the lengthened wavelength behind it. ## Related tools - [Audio Decrackler](https://elysiatools.com/en/tools/audio-decrackle): Remove crackles and subtle impulsive noise from audio files. 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