Case 1
- Source frequency
- 440Hz
- Speed of sound
- 343m/s
- Source speed
- 30m/s
- Which way is the source moving?
- Towards you
482.17Hz
Open with these valuesDoppler Effect Calculator
482.17Hz
Result: 482.17 HzA source moving towards you packs its wavefronts into a shorter gap, so the pitch rises; moving away it stretches them and the pitch drops. Approaching, divide by (v − vₛ); receding, divide by (v + vₛ). The listener stands still here — only the source moves.
The numbers at a glance
Held fixed: Source frequency 440.00 Hz, Speed of sound 343.00 m/s, Which way is the source moving? Towards you.
| Source speed (m/s) | Result (Hz) |
|---|---|
| 0.00 | 440.00 |
| 10.00 | 453.21 |
| 20.00 | 467.24 |
| 30.00Your value | 482.17 |
| 40.00 | 498.09 |
| 50.00 | 515.09 |
| 60.00 | 533.29 |
Worked examples
Case 2
- Source frequency
- 440Hz
- Speed of sound
- 343m/s
- Source speed
- 30m/s
- Which way is the source moving?
- Away from you
404.61Hz
Open with these valuesCase 3
- Source frequency
- 1000Hz
- Speed of sound
- 343m/s
- Source speed
- 50m/s
- Which way is the source moving?
- Towards you
1,170.65Hz
Open with these valuesHow it's calculated
f′ = f × v ÷ (v ∓ vₛ), minus approaching, plus receding
- StepEnter the frequency the source itself emits, in hertz.
- StepEnter the speed of sound: 343 m/s in air at 20 °C, 331 m/s at 0 °C.
- StepEnter how fast the source moves and pick towards or away.
- ResultRead the pitch a stationary listener hears.
What this number means
Only the source moves here
This page shifts the pitch for a moving source heard by a listener standing still, which is why there is no field for a listener speed. If the listener is the one moving, that is not the case this calculator covers.
Minus approaching, plus receding
The direction picks the sign in the denominator: (v − vₛ) towards you, (v + vₛ) away from you. Swap them and a 440 Hz horn at 30 m/s reads 404.61 Hz instead of 482.17 Hz.
The speed of sound is an input, not a constant
343 m/s is dry air at 20 °C and nothing else. It falls to about 331 m/s at 0 °C and to roughly 295 m/s at cruising altitude, while water carries sound at about 1481 m/s.
At the speed of sound there is no answer
For an approaching source the denominator (v − vₛ) reaches zero at exactly the speed of sound, and the result runs off to infinity. The wavefronts pile into a shock front — a sonic boom, not a pitch. A receding source has no such limit, because (v + vₛ) stays positive.
Commonly misread
I am driving towards a parked siren, so I enter my own speed as the source speed.
That field is the speed of the source, and this page holds the listener still. There is no field for a listener speed, so a moving listener is not the case covered here.
Approaching raises the pitch by as much as receding lowers it.
The shift is not symmetric. The same horn at 30 m/s is heard at 482.17 Hz coming towards you and 404.61 Hz going away, against 440 Hz at rest.
The source moves at 108 km/h, so I enter 108.
Both speeds go in as metres per second. Divide km/h by 3.6 first: 108 km/h is 30 m/s.
Reference table
| Source speed (m/s) | Towards you (Hz) | Away from you (Hz) |
|---|---|---|
| 0 | 440.00 | 440.00 |
| 10 | 453.21 | 427.54 |
| 30 | 482.17 | 404.61 |
| 60 | 533.29 | 374.49 |
| 100 | 621.07 | 340.68 |
Questions
How do I calculate the Doppler effect for an approaching source?
Multiply the source frequency by the speed of sound, then divide by the speed of sound minus the source speed: f′ = f × v ÷ (v − vₛ). For example, a 440 Hz horn approaching at 30 m/s with sound at 343 m/s gives 440 × 343 ÷ (343 − 30) = 482.17 Hz.
What is the Doppler effect?
The Doppler effect is the change in the frequency a stationary observer hears when a sound source moves relative to them. As the source approaches, the sound waves bunch up and the pitch rises; as it recedes, the waves spread out and the pitch drops. It is why a passing siren changes tone.
How do I handle a source moving away?
Set the direction to away from you and the calculator switches to a plus sign in the denominator: f′ = f × v ÷ (v + vₛ). The denominator is then larger than the speed of sound, so the observed frequency falls below the source frequency. A 440 Hz horn receding at 30 m/s with sound at 343 m/s gives 440 × 343 ÷ (343 + 30) = 404.61 Hz.
What speed of sound should I enter?
343 m/s is dry air at 20 °C, and that is the default here. It drops to about 331 m/s at 0 °C and to roughly 295 m/s in the cold thin air at cruising altitude, while water carries sound at about 1481 m/s. The speed of sound is a property of the medium and its temperature, not a universal constant.
What happens at and above the speed of sound?
For an approaching source the denominator (v − vₛ) reaches zero at exactly the speed of sound, and there is no observed frequency any more — the wavefronts pile up into a shock front and you get a sonic boom instead. Above it the formula returns a negative number, which is not a pitch. A receding source has no such limit, because (v + vₛ) always stays positive.
What units should I use?
Hertz for the source frequency and metres per second for both speeds. If a speed is given in km/h, divide by 3.6 before entering it.
Sources and last check
Information, not professional advice.