Ambulance 30 m/s toward you
f = 700 Hz, vs = 30, vo = 0 -> f′ ≈ 767 Hz.
Doppler effect calculator
Enter source frequency, source speed toward you, and observer speed toward the source. Blank c = 343 m/s (air).
Wavelength: λ = v/f. Wave speed: v = λ·f. Sound level: dB.
Result
Enter values. The result shows up here.
How it works
An ambulance comes toward you and the siren sounds higher. The source packs waves ahead of itself. The usual high-school 1D formula: f′ = f · (c + vo) / (c − vs). This is not relativistic radar, and not ultrasound at an angle: a straight line, for sound or water.
Sign: positive vs means the source approaches you. Positive vo means you walk toward the source. Both positive raise f′. Negative vs (the ambulance has passed) drops the pitch. With vs = vo = 0 you get f′ = f: a check that nothing shifts when both are still.
Default c = 343 m/s (air, about 20°C). Water sonar: type 1480. For radar or light you may enter c of light, but this non-relativistic model breaks when v is close to c.
We reject vs ≥ c, because the denominator c − vs would hit zero or go negative. The old shortcut f·(1+v/c) was only a small-v approximation; here you get the full ratio. Δf = f′ − f sits beside it: positive means a higher pitch.
Speeds follow the header (m/s or ft/s). f stays in Hz. A blank c means 343 m/s; blank vs or vo means zero.
How to use
- Enter source f in Hz (siren 700, tuning fork 440).
- Enter vs: positive when the source moves toward you; negative when it recedes.
- Enter vo or leave it blank if you stand still. Leave c blank for air.
Formula
f′ = f · (c + vo) / (c − vs)
Positive vs, vo: approach. vs < c. Blank c = 343 m/s.
Real-life examples
Ambulance receding
f = 700 Hz, vs = -30, vo = 0 -> f′ ≈ 644 Hz.
You walk toward the source
f = 440 Hz, vs = 0, vo = 2 -> f′ ≈ 443 Hz.
Both moving
f = 500 Hz, vs = 20, vo = 5 -> f′ ≈ 536 Hz.
Train 40 m/s
f = 440 Hz, vs = 40, vo = 0 -> f′ ≈ 498 Hz.
At rest
vs = vo = 0, f = 1000 Hz -> f′ = 1000 Hz.
Water, c = 1480
sonar f = 40000, vs = 5, c = 1480 -> f′ ≈ 40136 Hz.
Bike 8 m/s
f = 523 Hz, vs = 8, vo = 0 -> f′ ≈ 535 Hz.
Ways to use this calculator
- Ambulance siren: type 30 m/s toward you and compare f′ with 700 Hz at rest.
- Compare a fast approaching source with walking toward it: the source shifts pitch more.
- Sonar: c = 1480 m/s, small vs, see how tiny the f jump is in water.
Frequently asked questions
Which formula is used?
f′ = f·(c+vo)/(c−vs). Positive speeds mean approach. The usual 1D school formula, not one with a beam angle.
What if I leave c blank?
We use 343 m/s, a typical speed of sound in air at 20°C. In water type 1480.
Why can the source not catch c?
The denominator c − vs would hit zero. In this model the source does not catch its own wave; vs must stay below c.
Is this optical Doppler or GPS?
No. This is the classical version (sound, water). Light with v near c needs the relativistic formula, which is not here.
What does negative vs mean?
The source recedes from the observer. Waves stretch, pitch drops. Ambulance after it passes: vs negative.
Is wind in the model?
No. c is wave speed relative to a still medium. Wind would change effective c and needs a different model.
How is this different from f·(1+v/c)?
f·(1+v/c) is an approximation when v is much smaller than c. Here you get the full school ratio, better at a 30 m/s siren.
What is Δf next to the result?
It is f′ − f. Positive means higher pitch (approach). Negative means lower. At rest Δf = 0.
Can source f be zero?
No. Source frequency must be positive. Blank vs and vo are allowed and mean zero.
How do I get wavelength from f′?
Compute f′, then λ = c/f′ on the wavelength page, using the same c as here.