Doppler Effect Frequency Shift Calculator
When a sound source moves toward you, sound waves compress and pitch rises. When it moves away, waves stretch and pitch drops. This is the Doppler effect — and this calculator applies the exact classical formula so you can compute the perceived frequency in seconds. Works for ambulance sirens, radar guns, sonar, and physics homework. No login. No ads. Instant result.
The Doppler effect formula for sound is f' = f × (v + vo) / (v − vs) when approaching, or f' = f × (v − vo) / (v + vs) when receding, where v = speed of sound (343 m/s at 20 °C), vo = observer speed, vs = source speed. Example: an ambulance siren at 440 Hz approaching at 30 m/s is heard at 482 Hz — 42 Hz higher than the emitted tone.
When to use this calculator
- Physics students solving Doppler effect problems
- Engineers working on radar, sonar, or ultrasound systems
- Teachers demonstrating frequency shift with real numbers
- Checking how fast a vehicle is moving based on pitch change
- Astronomy problems involving redshift and blueshift
- Medical students studying Doppler ultrasound principles
Worked example: ambulance siren
- Source frequency: f = 440 Hz (A4 note)
- Source speed: vs = 30 m/s (108 km/h)
- Observer speed: vo = 0 m/s (standing still)
- Speed of sound: v = 343 m/s (20 °C air)
- Direction: approaching
- f' = 440 × (343 + 0) / (343 − 30) = 440 × 343 / 313 = 482.2 Hz
How it works
2 min readWhat Is the Doppler Effect?
The Doppler effect is the change in observed frequency of a wave caused by relative motion between the source and the observer. It applies to sound, light, radar, and any wave phenomenon.
The classic example: an ambulance emitting a constant 440 Hz siren sounds noticeably higher as it approaches, then drops as it passes and moves away.
The Doppler Effect Formula
Approaching: f' = f × (v + vo) / (v − vs)
Receding: f' = f × (v − vo) / (v + vs)
Where:
Common Examples Table
Ambulance siren (440 Hz, v = 343 m/s, observer stationary):
| Source speed (km/h) | Source speed (m/s) | Approaching — perceived Hz | Receding — perceived Hz | Pitch shift |
|---|---|---|---|---|
| 30 km/h | 8.3 m/s | 451 Hz | 430 Hz | +11 / −10 Hz |
| 60 km/h | 16.7 m/s | 463 Hz | 420 Hz | +23 / −20 Hz |
| 90 km/h | 25 m/s | 476 Hz | 411 Hz | +36 / −29 Hz |
| 108 km/h | 30 m/s | 482 Hz | 406 Hz | +42 / −34 Hz |
| 120 km/h | 33.3 m/s | 486 Hz | 404 Hz | +46 / −36 Hz |
Speed of Sound by Temperature
| Temperature | Speed of sound |
|---|---|
| 0 °C | 331 m/s |
| 10 °C | 337 m/s |
| 20 °C | 343 m/s |
| 30 °C | 349 m/s |
| 37 °C (body temperature) | 353 m/s |
Real-World Applications
Frequently asked questions
What is the Doppler effect formula for sound?
The Doppler formula is f' = f × (v + vo) / (v − vs) when the source approaches, and f' = f × (v − vo) / (v + vs) when it recedes. Here f is the emitted frequency, v is the speed of sound (343 m/s at 20 °C), vo is the observer's speed, and vs is the source's speed.
Why does an ambulance siren sound higher as it approaches?
As the ambulance moves toward you, each successive sound wave is emitted from a position slightly closer than the last, compressing the wave fronts. Your ear receives more wave cycles per second — a higher frequency. The effect reverses when it passes and recedes.
What speed of sound should I use?
Use 343 m/s for air at 20 °C (68 °F) — the standard room-temperature value. At 0 °C use 331 m/s; at 30 °C use 349 m/s. For water, sound travels at ~1480 m/s; for steel, ~5100 m/s.
What happens when the source moves at exactly the speed of sound?
The formula breaks down (division by zero) because all emitted waves pile up at the same point, forming a shock wave — the sonic boom. The classical Doppler formula only applies when the source speed is less than the speed of sound (subsonic conditions).
How do police radar guns use the Doppler effect?
Radar guns emit radio waves at a known frequency. The waves reflect off a vehicle and return with a Doppler-shifted frequency. The gun calculates the speed of the vehicle from the size of that frequency shift. The same principle applies to weather radar measuring precipitation speed.
How does Doppler ultrasound work in medicine?
A probe emits ultrasound at a fixed frequency (typically 2–10 MHz). Waves reflect off moving red blood cells and return at a slightly different frequency. The frequency shift reveals both the speed and direction of blood flow, allowing doctors to detect blockages, clots, or heart valve problems.
What is the difference between Doppler shift and redshift?
Redshift is the Doppler effect applied to light waves instead of sound. Galaxies moving away from Earth emit light at a lower frequency (shifted toward the red end of the spectrum). Astronomers use the amount of redshift to calculate how fast galaxies are receding and estimate the age and expansion rate of the universe.
Does the Doppler effect depend on which is moving — the source or the observer?
Yes — the formulas are not symmetric. If the source moves at 30 m/s toward a stationary observer, the result differs slightly from an observer moving at 30 m/s toward a stationary source. Both produce a higher perceived frequency, but the exact values differ. The full formula accounts for both velocities independently.
Can I use this calculator for light (electromagnetic waves)?
No — light requires the relativistic Doppler formula, which accounts for time dilation at speeds close to the speed of light. This calculator uses the classical acoustic formula, valid for sound waves in a medium at speeds well below the speed of sound.