Doppler Shift Calculator
Calculate the observed frequency due to the Doppler effect. Enter source frequency, source velocity, observer velocity and wave speed. Positive source velocity = source moving away; positive observer velocity = moving toward.
How to use this tool
- Enter source frequency f₀, source velocity vₛ, observer velocity vₒ and wave speed v in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your observed frequency and the full breakdown beneath it.
The Doppler effect shifts the observed frequency when source or observer are moving: f_obs = f₀ × (v + vₒ) / (v + vₛ). Approaching gives a higher (blue-shifted) frequency; receding gives a lower (red-shifted) frequency.
Formula
fobs = f0 × (vw + vo) ÷ (vw + vs)
Where: f0 = source frequency (Hz), vw = wave speed (m/s), vo = observer velocity (positive = toward source), vs = source velocity (positive = away from observer).
How it works
The Doppler effect describes the change in observed frequency of a wave when the source or observer is in relative motion. This calculator applies the classical Doppler formula with the sign convention that a positive observer velocity means moving toward the source and a positive source velocity means moving away from the observer.
The frequency shift Δf = fobs − f0 and percent change are also computed. The formula is valid for mechanical waves (sound, water) at speeds well below the wave speed; it does not apply to electromagnetic waves where relativistic Doppler equations are required.
Worked example
Worked example (stationary source and observer)
- Given: source frequency f₀ = 440 Hz, source velocity vₛ = 0 m/s, observer velocity vₒ = 0 m/s, wave speed vᵤ = 343 m/s (speed of sound in air).
- Apply formula: fᵒᵇₛ = 440 × (343 + 0) / (343 + 0) = 440 × 1 = 440 Hz.
- Frequency shift: Δf = 440 − 440 = 0 Hz.
Observed frequency = 440 Hz; frequency shift Δf = 0 Hz (no Doppler effect when both are stationary).
Common mistakes to avoid
- Getting the sign convention backwards: a source moving toward the observer uses a negative source velocity in the standard formula, not positive. Entering the wrong sign flips the result from a blue-shift to a red-shift.
- Using the relativistic Doppler formula for everyday sound problems. This calculator uses the classical formula and assumes wave speeds well below the speed of light or sound.
- Entering the observer speed as negative when the observer moves away, which is the correct convention, then being surprised the observed frequency is lower than the source frequency.
Key terms
- Doppler effect
- The change in observed frequency of a wave caused by relative motion between the source and observer.
- Blue shift
- An increase in observed frequency (and energy) occurring when a source and observer approach each other.
- Red shift
- A decrease in observed frequency occurring when a source and observer move apart; widely used in astronomy to measure galactic recession.
- Wave speed (vᵤ)
- The speed at which a wave propagates through a medium. For sound in air at 20°C, this is approximately 343 m/s.
- Frequency shift (Δf)
- The difference between the observed and source frequencies; positive indicates blue-shift, negative indicates red-shift.
Frequently asked questions
- What is the speed of sound used here?
- 343 m/s at 20 °C in air at sea level. It varies with temperature: roughly v ≈ 331 + 0.6×T(°C) m/s.
- Does the Doppler effect apply to light too?
- Yes, but the relativistic formula must be used. The astronomical redshift of distant galaxies is a Doppler-related phenomenon.