Doppler Effect Calculator
Find the observed frequency from a moving source.
Defaults to 343 m/s (air at 20°C).
Results update as you type.
How it works
The Doppler effect is the change in the frequency of a wave that an observer detects when the source is moving relative to them. This Doppler effect calculator computes the observed frequency for sound from a moving source and a stationary observer, using the source frequency, the source's speed, the speed of sound, and whether the source is approaching or receding. It is the physics behind the familiar rise and fall in pitch of a passing siren or racing car. This matters well beyond everyday sound. Doppler radar tracks the motion of storms and speeding vehicles, medical ultrasound measures blood flow, and astronomers use the Doppler shift of light to discover that distant galaxies are receding, evidence that the universe is expanding. Understanding how motion shifts frequency lets engineers and scientists turn a pitch or colour change into a precise measurement of speed. The formula works because a source moving toward you emits each wave crest from a slightly closer position, bunching the waves into a higher frequency, while a receding source stretches them into a lower one. Selecting the direction tells the calculator whether to divide by the speed of sound minus or plus the source speed. Physics students, engineers, and anyone curious about that shifting siren pitch rely on a Doppler effect calculator to quantify exactly how much the frequency changes.
approaching: f' = f · c/(c − vₛ) · receding: f' = f · c/(c + vₛ)
The Doppler effect changes the frequency an observer hears because a moving source compresses the sound waves ahead of it and stretches those behind it. When the source approaches, each successive wave crest is emitted a little closer, so the waves bunch up, the wavelength shortens, and the observed frequency rises; dividing by (c minus the source speed) captures this compression. When the source recedes, the crests spread out and the frequency drops, so the formula divides by (c plus the source speed). The speed of sound sets how fast the waves travel relative to the moving source.
Source:Standard physics (Doppler effect)
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter source frequency, source speed and source direction.
- 2
Adjust the options
Adjust speed of sound if they apply — sensible defaults are already set.
- 3
Read your result
Observed frequency updates instantly as you type — no button to press.
Frequently asked questions
Why does a passing siren change pitch?
As an emergency vehicle approaches, its sound waves are compressed into a shorter wavelength, raising the frequency you hear so the siren sounds higher pitched. The instant it passes and starts moving away, the waves stretch out, lowering the frequency and dropping the pitch. The abrupt shift you notice as the vehicle goes by is the Doppler effect switching from the approaching case to the receding case in real time.
Does this calculator assume the observer is stationary?
Yes. This version models a moving source and a stationary observer, which covers the most common situations like a passing siren or car heard by someone standing still. If the observer is also moving, the full Doppler formula adds terms for the observer's velocity as well. For a first analysis, the stationary-observer case captures the essential frequency shift and is accurate whenever you are not moving toward or away from the source.
What speed of sound should I use?
The speed of sound in air is about 343 metres per second at 20 degrees Celsius, which is this calculator's default. It rises with temperature, reaching roughly 349 metres per second at 30 degrees and falling to about 331 at freezing. Sound also travels much faster in water, around 1,480 metres per second, and faster still in solids, so adjust the value if your medium is not room-temperature air.
What happens as the source approaches the speed of sound?
As the source speed nears the speed of sound, the denominator in the approaching formula shrinks toward zero, so the observed frequency climbs steeply toward very high values. Physically, the waves pile up almost on top of one another just ahead of the source. When the source actually reaches the speed of sound, the waves stack into a shock wave, producing the sonic boom heard when aircraft break the sound barrier.
Does the Doppler effect apply to light too?
Yes. Light waves shift in frequency with relative motion just as sound does, though the exact formula involves relativity. A source moving away shifts light toward the red end of the spectrum, a redshift, while an approaching source causes a blueshift. Astronomers measure these shifts to determine how fast stars and galaxies move, and the widespread redshift of distant galaxies is key evidence that the universe is expanding.