Frequency Doppler Effect Calculator

Calculation type

Pick the model that matches your wave and speed.

Emitted frequency f₀ *

Enter a valid positive frequency.

Display frequency unit

This affects displayed f₀, f′, and Δf.

Medium

Wave speed depends on the medium.

Air temperature

°C

Uses v ≈ 331.3 + 0.606·T.

Custom wave speed v

Used only for “Custom wave speed”.

Observer speed vₒ

Speed magnitude. Direction is set separately.

Observer direction

Toward increases f′, away reduces f′.

Source speed vₛ

Keep |vₛ| less than the wave speed.

Source direction

Toward increases f′, away reduces f′.

Tip: For a stationary observer or source, set its speed to 0.

Relative speed |u| *

Enter line-of-sight relative speed magnitude.

Relative motion

Applies the relativistic Doppler factor.

Note: Valid for light/EM when speeds are significant.

Formula used

Sound (classical Doppler)

f′ = f₀ · (v + vₒ) / (v − vₛ)

v is wave speed in the medium, vₒ is observer velocity toward the source, and vₛ is source velocity toward the observer. Use negative directions for motion away.

Relativistic (light / EM)

f′ = f₀ · √((1 ± β)/(1 ∓ β)), β = u/c

Choose “Approaching” for the + sign (higher frequency) and “Receding” for the − sign (lower frequency).

Wavelength is computed by λ = v/f for sound, and λ = c/f for EM. Frequency shift is Δf = f′ − f₀, and percent shift is 100·Δf/f₀.

How to use this calculator

Choose Sound in a medium or Relativistic (light / EM).
Enter emitted frequency f₀ and select its unit.
For sound, select a medium (or set a custom wave speed).
Enter observer and source speeds, then choose their directions.
For relativistic mode, enter the relative speed and motion type.
Press Calculate to see results above the form.
Use the download buttons to export your result.

Example data table

Case	Model	Inputs	Observed frequency
1	Sound	f₀=1000 Hz, air 20°C, vₒ=0, vₛ=30 m/s toward	≈ 1095.0 Hz
2	Sound	f₀=500 Hz, air 20°C, vₒ=15 m/s toward, vₛ=0	≈ 521.9 Hz
3	Relativistic	f₀=100 MHz, u=0.1c approaching	≈ 110.55 MHz
4	Relativistic	f₀=5.00×10¹⁴ Hz, u=30,000 km/s receding	≈ 4.54×10¹⁴ Hz

Values are rounded for readability. Your calculator outputs more precision.

Doppler frequency shift overview

The Doppler effect describes how a measured frequency changes when a source and observer move along the line of sight. Approaching motion raises the observed frequency, while separating motion lowers it quickly.

What inputs matter most

Enter an emitted frequency f₀, then describe motion. For sound, select the medium speed (air, water, steel, or custom). For light and other EM waves, enter a relative speed and choose approaching or receding. Unit selectors keep everything consistent. You can also choose the display unit (Hz, kHz, MHz, GHz) so the results match lab notes, audio specs, or RF documentation.

Sound model in a real medium

In the classical sound model, the medium sets the wave speed v. Typical values are about 343 m/s in air near room conditions, roughly 1482 m/s in water, and near 5960 m/s in steel. Since sound needs a medium, v strongly controls the shift.

Temperature effect in air

Air temperature changes the speed of sound. The calculator uses v ≈ 331.3 + 0.606·T (m/s). At 0°C v≈331.3 m/s, at 20°C v≈343.4 m/s, and at 40°C v≈355.5 m/s. Higher v usually means a smaller percentage shift for the same speeds.

Observer vs source motion

Sound Doppler depends on observer speed vₒ and source speed vₛ. A moving observer changes how quickly wavefronts are encountered, while a moving source changes wavefront spacing. The direction menus apply the sign: “toward” increases f′ and “away” decreases f′.

Relativistic mode for EM waves

For EM waves the speed is constant at c = 299,792,458 m/s, so the correct shift uses the relativistic Doppler factor with β = u/c. At u = 0.1c approaching, the factor is about 1.1055, so 100 MHz becomes about 110.55 MHz.

Reading the outputs

Results include observed frequency f′, shift Δf, percent shift, and wavelength values (meters and nanometers when relevant). For sound, wavelength uses λ = v/f; for EM, λ = c/f. Positive Δf indicates a higher observed frequency; negative Δf indicates a lower one. Percent shift helps compare scenarios across different base frequencies.

Practical checks and limits

For the sound model, keep |vₛ| below v so the denominator v − vₛ remains valid. Sirens (500–2000 Hz) with vehicle speeds (10–40 m/s) often shift by tens of hertz in everyday traffic. For radio and radar (MHz–GHz), small speeds can matter, while relativistic effects become important only at very high fractions of c.

FAQs

1) Why does approaching motion raise the frequency?
Because wavefronts reach the observer more often, so more cycles arrive per second.

2) Can I set the observer speed to zero?
Yes. Set vₒ to 0 for a stationary observer and model only the source motion.

3) What if both are moving away?
Choose “away” for both directions. The sign convention produces a lower observed frequency.

4) Why does the calculator warn when vₛ ≥ v?
The classical model breaks down near the wave speed, and v − vₛ becomes invalid.

5) When should I use relativistic mode?
Use it for light, radio, or any EM wave, especially when u is not tiny compared with c.

6) What does wavelength output help me understand?
It shows how the spacing between wave peaks changes for acoustics, optics, and antennas.

7) Are the built-in medium speeds exact?
They are typical reference values. Use “Custom wave speed” for known materials and conditions.