Doppler Effect Calculator

The Doppler Effect Calculator computes the frequency, wavelength, and pitch that an observer detects when a sound or light source is moving — or when the observer themselves is moving. Pick a wave medium, type the source frequency and speeds, choose direction, and see the result, wave-front animation, and (for audible frequencies) an actual audio playback of the shifted pitch.

How to Use This Doppler Effect Calculator

1. Choose the Doppler mode. Pick Classical for sound, water, or any mechanical wave. Pick Relativistic for light, radio, and radar.
2. Pick the wave medium — air at 20 °C, helium, fresh or sea water, steel, or vacuum. You can also enter a custom wave speed.
3. Enter the source frequency in hertz. The result automatically switches to kHz, MHz, GHz, or THz as needed.
4. Set the source speed, then click a direction chip: → Toward the observer, ← Away, or ● Still. Do the same for the observer.
5. Press Calculate and read the observed frequency, frequency shift, wavelength change, animated wave fronts, and (for audible-range tones) play the actual pitch difference.

What Makes This Calculator Different

The Doppler Effect Formula

For a classical wave (sound, water, ultrasound, or any mechanical wave) the observed frequency \(f_o\) is

\[ f_o \;=\; f_s \cdot \dfrac{c + v_o}{c - v_s} \]

where \(f_s\) is the source frequency, \(c\) is the wave speed in the medium, \(v_o\) is the observer speed (positive when the observer moves toward the source), and \(v_s\) is the source speed (positive when the source moves toward the observer). For light or any electromagnetic wave, the relativistic Doppler formula is used:

\[ f_o \;=\; f_s \cdot \sqrt{\dfrac{1 + \beta}{1 - \beta}} \quad\text{with}\quad \beta = \dfrac{v_{rel}}{c} \]

Here \(v_{rel}\) is the line-of-sight relative velocity (positive when the source and observer are approaching), and \(c\) is the speed of light, 299,792,458 m/s. The relativistic formula is symmetric in source and observer motion, but the classical formula is not — a moving source produces a different shift than a moving observer at the same speed.

Wave Speeds Used in This Calculator

Worked Example: Police Siren

An ambulance siren emits 700 Hz and approaches a stationary listener at 90 km/h ≈ 25 m/s through air at 20 °C (c = 343 m/s).

• Source speed toward observer: \(v_s = +25\) m/s. Observer is stationary: \(v_o = 0\).
• \(f_o = 700 \cdot \dfrac{343 + 0}{343 - 25} = 700 \cdot \dfrac{343}{318} \approx 755.0\) Hz.
• Frequency shift \(\Delta f \approx +55\) Hz (+7.9%). In musical terms, that's about 1.3 semitones higher.
• After it passes and is now receding, the formula flips: \(v_s = -25\) m/s gives \(f_o \approx 652\) Hz. The total drop you hear as it goes by is about 103 Hz (around 2.5 semitones), exactly the swoop that makes sirens so recognizable.

Why the Sound of a Passing Car Drops in Pitch

As the car approaches, every successive wave crest is emitted slightly closer to you than the previous one — so the crests bunch up, arriving at your ear more frequently than they were emitted. After it passes, each crest is born farther from you than the last, so they spread out and arrive less frequently. The peak (when the car is right next to you) is when the apparent frequency changes most quickly — that's what gives the siren its dramatic "wee-OOO" swoop, even though the source keeps emitting one steady tone.

Blueshift, Redshift, and Cosmology

In astronomy the Doppler effect lets us measure how fast stars and galaxies are moving toward or away from us. Light from a galaxy moving away is "redshifted" — its spectral lines shift to longer wavelengths (lower frequencies). Light from a galaxy moving toward us is "blueshifted." Edwin Hubble's 1929 observation that distant galaxies are systematically redshifted, with shift proportional to distance, is one of the foundational pieces of evidence for the expansion of the universe.

Doppler Radar and Police Speed Guns

A radar gun transmits microwaves at a fixed frequency (often around 10 GHz, 24 GHz, or 35 GHz). The waves bounce off a moving vehicle and return Doppler-shifted twice — once on the way out and once on the way back. The radar gun measures the frequency shift of the round trip and converts that into a vehicle speed. The classical low-speed approximation works fine here because vehicle speeds are tiny compared to the speed of light, but a serious system uses the relativistic formula to stay accurate.

Frequently Asked Questions

What is the Doppler effect in simple terms?
It is the change in the frequency or pitch of a wave that an observer hears or measures, caused by the source or observer moving relative to each other. Approaching motion raises the pitch (or shortens the wavelength); receding motion lowers the pitch (lengthens the wavelength).

Why does the pitch of a siren change as it passes?
As the siren approaches you, each successive wave crest is emitted from a position closer to you. The crests reach your ear more often per second, which sounds like a higher pitch. After it passes and is moving away, the crests are spread out and you hear a lower pitch.

What is blueshift and redshift?
Blueshift means the observed frequency is higher and the wavelength shorter than what the source emits, which happens when source and observer are approaching. Redshift is the opposite. Astronomers use the redshift of distant galaxies as evidence the universe is expanding.

When should I use the relativistic mode?
Use the relativistic mode for light, radio, and radar, and any time the relative speed is more than a few percent of the speed of light. For everyday sound situations the classical mode is exact.

Why does the calculator say sonic boom regime?
In the classical formula the denominator becomes zero or negative when the source matches or exceeds the wave speed. At and above the wave speed all wave fronts pile into a shock cone — a sonic boom — and a single observed frequency no longer makes physical sense.

Can I hear the pitch change?
Yes. When both the source frequency and the observed frequency fall in the human hearing range (about 20 Hz to 20 kHz), the result section shows Play buttons that use the browser's Web Audio API to synthesize the actual pure tones, plus a smooth sweep from one to the other.

Does this calculator work for water and helium?
Yes. Pick the matching medium and the calculator uses the correct speed of sound in that medium. Sonar systems, dolphin communication, and even "helium voice" experiments all follow the same Doppler formula, just with a different wave speed.