Doppler Effect Calculator
doppler effect calculator. Get instant, accurate results. Enter values for instant results with step-by-step formulas.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator
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.
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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