Doppler Effect Calculator
Calculate the observed frequency shift when a sound source or observer is moving, using a speed of sound of 343 m/s at 20 degrees Celsius.
Doppler Effect Calculator
Calculator
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Formula: f' = f × (v + v_observer) / (v - v_source)
Worked example — 482.4 Hz
Formula
f' = f × (v + v_observer) / (v - v_source)
Frequency shift when source or observer moves. v_sound = 343 m/s at 20°C.
Worked Examples
Example 1: Approaching car horn
Problem:f=440Hz, source approaching at 30 m/s
Solution:f'=440×343/(343-30)=482.4 Hz
Result:482.4 Hz
Frequently Asked Questions
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. The formula is f' = f × (v + v_observer) / (v − v_source), where v = 343 m/s is the speed of sound at 20°C. Moving toward each other raises the pitch; moving apart lowers it.
How do you calculate the observed Doppler frequency?
Use f' = f × (v + v_o) / (v − v_s). Example: a source at f = 440 Hz approaches at v_s = 30 m/s with the observer stationary: f' = 440 × 343 / (343 − 30) = 440 × 343 / 313 ≈ 482.1 Hz. As the source recedes at 30 m/s: f' = 440 × 343 / (343 + 30) ≈ 409.4 Hz — a noticeable drop.
What units does the Doppler effect calculator use?
Source frequency is in hertz (Hz), and source and observer velocities are in meters per second (m/s). Positive velocity means approaching; negative means receding. The speed of sound is fixed at 343 m/s (dry air, 20°C). Output shows observed frequency (Hz) and the percentage shift.
Why do ambulance sirens change pitch as they pass?
As the ambulance approaches, sound waves are compressed — shortening their wavelength and raising frequency (blue-shift). As it passes and recedes, waves are stretched — increasing wavelength and lowering frequency (red-shift). The actual siren frequency is constant; only your perception changes due to wave compression and expansion.
What is the difference between a moving source and a moving observer?
Both raise the pitch when closing the gap, but they enter f' = f(v + v_o)/(v - v_s) differently. A moving source physically compresses the emitted wavelength, so it sits in the denominator; a moving observer simply sweeps through wavefronts faster, so it sits in the numerator. At 440 Hz and 30 m/s the source case gives 440 x 343/313 = 482.1 Hz, while the observer case gives 440 x 373/343 = 478.5 Hz - close, but not identical.
Why does the formula break down when the source reaches the speed of sound?
As v_s approaches 343 m/s the denominator (v - v_s) approaches zero and the predicted observed frequency diverges. Physically the wavefronts no longer spread ahead of the source; they pile up into a single conical shock front, the Mach cone, heard as a sonic boom. Once the Mach number v_s/v reaches 1 the ordinary Doppler relation stops describing the situation, which is why the calculator flags that condition instead of returning a number.
How does air temperature change the speed of sound used in the shift?
The 343 m/s value applies to dry air near 20 C. Sound speed rises with temperature, closely approximated by v = 331 + 0.6 x T(C) m/s, so 0 C gives about 331 m/s and 35 C about 352 m/s. Because v appears in both the numerator and the denominator, a wrong sound speed shifts the result only slightly for modest source speeds, but the error grows as v_s becomes a large fraction of v.
When should the relativistic Doppler formula be used instead of this one?
Use the relativistic form for light and other electromagnetic waves, where there is no medium and the observed shift depends only on relative velocity. For a receding source it is f' = f x sqrt((1 - B)/(1 + B)) with B = v/c. Astronomers quote the result as redshift z, the fractional change in wavelength. The acoustic formula used here assumes a medium at rest and speeds far below the speed of light.
How is the Doppler shift expressed in wavelength rather than frequency?
Because v = f x lambda, a source approaching at v_s emits successive wavefronts that are closer together: lambda' = (v - v_s)/f. A stationary observer then hears f' = v/lambda' = f x v/(v - v_s), which is exactly the frequency form. Thinking in wavelengths makes the physical picture clearer - the wave crests bunch up ahead of the source and stretch out behind it.
How fast must a source move for the pitch change to be a full semitone?
A semitone is a frequency ratio of 2^(1/12) = 1.0595. Setting v/(v - v_s) = 1.0595 gives v_s = 343 x (1 - 1/1.0595) = 19.3 m/s, roughly 69 km/h. That is why a car passing at highway speed produces a pitch drop of well over a semitone as it goes from approaching to receding, while a jogger carrying a speaker produces a shift far too small to name as a musical interval.
Background & Theory
The Doppler Effect Beyond Sirens
The Doppler effect is often introduced with a passing ambulance, but the same math (with the appropriate wave speed substituted in) governs radar guns, weather radar, astronomical redshift, and medical ultrasound. What changes between these applications is only the wave speed and the typical source/observer velocities involved — the underlying relationship f' = f(v ± v_o)/(v ∓ v_s) is identical.
| Application | Wave type | What's measured |
|---|---|---|
| Passing ambulance siren | Sound (343 m/s) | Audible pitch shift, a few percent typically |
| Police radar gun | Radio/microwave (light speed) | Reflected frequency shift converted to vehicle speed |
| Astronomical redshift | Light | Recession velocity of distant galaxies, evidence for cosmic expansion |
| Medical Doppler ultrasound | Ultrasound (in tissue) | Blood flow speed and direction in vessels |
At everyday vehicle speeds (tens of m/s) the sound-based Doppler shift is only a few percent, which is why it's noticeable but not dramatic. Astronomical redshifts can approach or exceed the speed of light's fraction v/c for very distant objects, requiring the relativistic Doppler formula instead of the simple acoustic one used here.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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