Enter the emitted frequency, wave velocity, source velocity, and observer velocity to calculate the observed (Doppler-shifted) frequency. The Doppler Effect Calculator applies the classic Doppler shift formula and returns the apparent frequency, frequency shift, and percent change — perfect for physics problems involving moving ambulances, trains, or any wave source.
Observed Frequency (f′)
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Frequency Shift (Δf)
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Percent Change
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Shift Type
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The Doppler effect is the change in observed frequency of a wave when the source or the observer is in motion relative to the medium. When the source approaches the observer, the frequency appears higher (blueshift for light, higher pitch for sound). When it moves away, the observed frequency is lower (redshift or lower pitch).
The Doppler shift formula is f′ = f₀ × (v + vₒ) / (v + vₛ), where f₀ is the emitted frequency, v is the wave velocity in the medium, vₒ is the observer velocity (positive toward source), and vₛ is the source velocity (positive away from observer). Sign conventions depend on direction of motion.
The default wave velocity is 343 m/s, which is the approximate speed of sound in dry air at 20°C (68°F). You can adjust this value for different temperatures or mediums — for example, sound travels at about 1,480 m/s in water.
When the source moves toward the observer, the sound waves are compressed, resulting in a higher observed frequency than the emitted frequency. This is why a siren sounds higher-pitched as an ambulance approaches you.
When the source moves away from the observer, the sound waves are stretched, reducing the observed frequency below the emitted frequency. This explains why an ambulance siren sounds lower-pitched after it passes you.
Yes. If the observer is moving toward the source, they intercept wave crests more frequently, increasing the observed frequency. If they move away from the source, the observed frequency decreases. Both source and observer velocities contribute to the total Doppler shift.
Yes, but light requires a relativistic treatment since it does not travel through a medium. For light, the redshift (recession) and blueshift (approach) are described by the relativistic Doppler formula. This calculator focuses on the classical (acoustic/sound) Doppler effect.
The emitted frequency (f₀) is the true frequency produced by the source when both source and observer are stationary. The observed (or apparent) frequency (f′) is what the observer actually detects due to relative motion. The difference between them is the Doppler shift (Δf = f′ − f₀).