Aaron Graves, PhDude (Replica)

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doppler shift calculator

Posted on February 16, 2026 by Admin
f′ = f₀ × (v + vo) / (v − vs)
Use 343 m/s for sound in dry air at ~20°C.
Positive = observer moving toward source, negative = moving away.
Positive = source moving toward observer, negative = moving away.
Enter values and click Calculate to see the observed frequency and shift.

What is the Doppler shift?

The Doppler shift is the change in observed frequency caused by relative motion between a wave source and an observer. If they move toward each other, observed frequency increases. If they move apart, observed frequency decreases.

You hear this effect every time an ambulance passes: the siren sounds higher in pitch as it approaches and lower after it passes. The same concept applies to light, where astronomers call upward frequency shifts blueshift and downward shifts redshift.

Formulas used in this calculator

1) Sound in a medium (classical Doppler)

For sound waves in air (or another medium), this page uses:

f′ = f₀ × (v + vo) / (v − vs)

  • f₀: emitted/source frequency
  • f′: observed frequency
  • v: wave speed in the medium
  • vo: observer speed (positive toward source)
  • vs: source speed (positive toward observer)

2) Light and electromagnetic waves (relativistic Doppler)

For high-speed motion involving light, relativity matters. This calculator uses:

f′ = f₀ × √((1 + β)/(1 − β)), with β = v/c

  • v: radial relative velocity
  • c: speed of light (299,792,458 m/s)
  • Positive v means approaching; negative means receding.

How to use this Doppler shift calculator

  1. Select Sound or Light mode.
  2. Enter the original frequency in hertz (Hz).
  3. Enter the motion values using the sign conventions shown below each field.
  4. Click Calculate to get observed frequency, absolute shift, and percent change.
Tip: If your result is unexpectedly negative or extremely large in sound mode, check your sign choices and ensure the denominator term (v − vs) stays positive and nonzero.

Worked examples

Example A: Siren approaching

Suppose a siren emits 700 Hz, the speed of sound is 343 m/s, observer is still, and source moves toward observer at 25 m/s. The observed frequency becomes higher than 700 Hz, which matches the familiar rising pitch.

Example B: Galaxy moving away

If a light source recedes, enter a negative relative speed in light mode. The calculator returns a lower observed frequency (redshift), which is central to modern cosmology and expansion measurements.

Real-world applications

  • Police radar and speed enforcement
  • Medical ultrasound blood-flow estimation
  • Weather Doppler radar for storm velocity
  • Astronomy: redshift/blueshift of stars and galaxies
  • Sonar and acoustic tracking

Common mistakes to avoid

  • Mixing sign conventions (toward vs away)
  • Using km/h in one field and m/s in another
  • Applying classical sound formula to high-speed light problems
  • Entering |v| ≥ c in relativistic mode

Quick FAQ

Does amplitude affect Doppler shift?

No. Doppler shift is about frequency change due to relative motion, not loudness.

Can both source and observer move?

Yes. In sound mode this calculator explicitly handles both motions.

Is this useful for wavelength too?

Yes. Once you have observed frequency, wavelength follows from λ = wave speed / frequency in the relevant model.

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