Doppler Effect Calculator

How to Use This Calculator

1. Enter source frequency f₀ (e.g. 440 Hz for concert A).
2. Enter source velocity v_s — positive means the source is approaching the observer.
3. Enter wave speed c (343 m/s for sound in air at 20°C; use 3×10⁸ m/s for light).
4. Use Observer Moving or Both Moving tabs for the respective scenarios.
5. Professional mode adds redshift z, radar speed, and Mach number.

Formula

Example

Frequently Asked Questions

• What is the Doppler effect? ▼
  The Doppler effect is the change in observed frequency when a source or observer moves relative to the medium. Approaching source: f′ = f₀ × c/(c − v_s) — higher pitch. Receding source: denominator grows → lower pitch. Classic example: ambulance siren.
• What formula is used for a moving observer? ▼
  f′ = f₀ × (c + v_o) / c. Positive v_o = observer approaching source → higher frequency. Negative v_o = receding → lower. If both source and observer move: f′ = f₀ × (c + v_o) / (c − v_s).
• What is redshift z? ▼
  z = Δλ/λ₀ = (λ_obs − λ_em)/λ_em. Positive z = object receding (light shifted to red/longer wavelength). Negative = blueshifted (approaching). Used in astronomy to measure galaxy recession speed. z = 0.1 means galaxy moves at ~10% speed of light (non-relativistic).
• How does Doppler radar measure speed? ▼
  Radar sends a wave at frequency f₀, reflects off a moving target. The round-trip Doppler shift doubles: Δf = 2v/λ. Solving: v = Δf × c / (2f₀). Police radar and weather Doppler radar both use this. The 'both moving' formula applies (radar is source and receiver).
• What is the relativistic Doppler formula? ▼
  For light (v near c), the classical formula fails. Relativistic: f′ = f₀ × √((1 + β)/(1 − β)) for approaching source, where β = v/c. The classical formula underestimates shift at high velocities. Important for GPS satellite corrections and astronomical spectra.

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