What is the Doppler effect?

The Doppler effect is the change in observed frequency of a wave when the source and observer are moving relative to each other. If they approach, the observed frequency is higher than the emitted frequency; if they recede, it is lower.

What formula is used for sound?

The classical Doppler formula is f_o = f_s × (v + v_o) / (v + v_s), where f_s is the source frequency, v is the wave speed in the medium, v_o is the observer speed (positive toward source), and v_s is the source speed (positive away from observer).

What formula is used for light?

For electromagnetic waves, the relativistic Doppler formula is used: f_o = f_s × sqrt((1 − β) / (1 + β)), where β = v/c and v is the relative velocity between source and observer (positive = receding). This accounts for time dilation.

What does a positive frequency shift mean?

A positive shift (f_o > f_s) means the source and observer are approaching — a blueshift for light or a higher pitch for sound. A negative shift (f_o < f_s) means they are moving apart — a redshift for light or a lower pitch for sound.

What wave speed should I use for sound?

In dry air at 20 °C the speed of sound is approximately 343 m/s. It increases with temperature (roughly 0.6 m/s per °C) and varies in other media: about 1480 m/s in water and 5100 m/s in steel.

Can this calculator handle supersonic speeds?

For the classical sound formula, source speeds at or above the wave speed produce a Mach cone and the standard Doppler formula breaks down. The calculator will show a warning in that case. For light, speeds are always below c, so the relativistic formula always applies.

Doppler Effect Calculator

Name: Doppler Effect Calculator
Availability: InStock
Author: Nham Vu

Enter the source frequency and relative velocities of the source and observer to instantly calculate the Doppler-shifted observed frequency.

Wave Type

Parameters

Source Frequency (Hz)

Wave Speed in Medium (m/s)

Air 20°C: 343 m/s | Water: 1480 m/s | Steel: 5100 m/s

Observer Speed (m/s)

Source Speed (m/s)

Quick Presets

Results

Enter a source frequency and velocities to see the Doppler shift.

Formula Used

f_o = f_s × (v + v_o) / (v + v_s)

f_s = source frequency | v = wave speed
v_o = observer speed (+ toward source, − away)
v_s = source speed (+ away from observer, − toward)

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Summary

Enter the source frequency and relative velocities of the source and observer to instantly calculate the Doppler-shifted observed frequency.

How it works

Select the wave type: Sound (classical Doppler) or Light (relativistic Doppler).
Enter the source frequency in Hz (or use the preset examples).
For sound: set the wave speed in the medium (default 343 m/s for air at 20 °C).
Enter the speed of the source and observer in m/s, and select their direction of motion.
The calculator applies the Doppler formula and displays the observed frequency, frequency shift, and change in wavelength.

Use cases

Determine the pitch change of a passing ambulance siren.
Calculate radar gun frequency shifts for speed measurement.
Compute astronomical redshift or blueshift for moving stars and galaxies.
Analyze sonar return frequencies in underwater acoustics.
Verify physics homework problems on wave frequency shifts.
Explore how relative speed affects the perceived pitch of sound.
Calculate Doppler shifts in medical ultrasound imaging.
Understand the relationship between motion direction and frequency change.

Frequently Asked Questions

Last updated: 2026-06-13 · Reviewed by Nham Vu